双椭圆外切内接N边形问题

数学星空 · 发表于 2014-4-29 22:34:29

mathe 发表于 2014-4-29 13:21
其中假设特征方程为\(f(x)=x^3+u_2x^2+u_1x+u_0\)

此处特征根为\(r_1,r_2,r_3\)吧？
否则与我得到的结果刚好是\({a 与 m}，{b与n}\)互换才是一致的。

数学星空 · 发表于 2014-4-30 00:09:39

根据mathe提供的椭圆曲线理论算出结果与我得到的结果一致，现根据椭圆曲线理论算出的\(k=3\sim 13\),双椭圆内接外切\(k\)边形的条件或者说封闭指数为\(k\)的条件为：

有兴趣的可以对照一下18#，\(k=3\sim 8\)的结果

\(k=3\)时

\(an+bm-mn=0\)

\(k=4\)时

\(a^2n^2+b^2m^2-m^2n^2=0\)

\(k=5\)时

\(a^3n^3-a^2bmn^2+a^2mn^3-ab^2m^2n+2abm^2n^2-am^2n^3+b^3m^3+b^2m^3n-bm^3n^2-m^3n^3=0\)

\(k=6\)时

\(a^4n^4-2a^2b^2m^2n^2+2a^2m^2n^4+b^4m^4+2b^2m^4n^2-3m^4n^4=0\)

\(k=7\)时

\(a^6n^6+2a^5bmn^5-2a^5mn^6-a^4b^2m^2n^4+2a^4bm^2n^5-a^4m^2n^6-4a^3b^3m^3n^3+4a^3m^3n^6-a^2b^4m^4n^2+2a^2b^2m^4n^4-a^2m^4n^6+2ab^5m^5n+2ab^4m^5n^2-2abm^5n^5-2am^5n^6+b^6m^6-2b^5m^6n-b^4m^6n^2+4b^3m^6n^3-b^2m^6n^4-2bm^6n^5+m^6n^6=0\)

\(k=8\)时

\(a^8n^8+4a^6b^2m^2n^6-4a^6m^2n^8-10a^4b^4m^4n^4+4a^4b^2m^4n^6+6a^4m^4n^8+4a^2b^6m^6n^2+4a^2b^4m^6n^4-4a^2b^2m^6n^6-4a^2m^6n^8+b^8m^8-4b^6m^8n^2+6b^4m^8n^4-4b^2m^8n^6+m^8n^8=0\)

\(k=9\)时

\(a^9n^9-3a^8bmn^8+3a^8mn^9+8a^6b^3m^3n^6+4a^6b^2m^3n^7-4a^6bm^3n^8-8a^6m^3n^9-6a^5b^4m^4n^5+12a^5b^2m^4n^7-6a^5m^4n^9-6a^4b^5m^5n^4-14a^4b^4m^5n^5-8a^4b^3m^5n^6+8a^4b^2m^5n^7+14a^4bm^5n^8+6a^4m^5n^9+8a^3b^6m^6n^3-8a^3b^4m^6n^5-8a^3b^2m^6n^7+8a^3m^6n^9+4a^2b^6m^7n^3+12a^2b^5m^7n^4+8a^2b^4m^7n^5-8a^2b^3m^7n^6-12a^2b^2m^7n^7-4a^2bm^7n^8-3ab^8m^8n-4ab^6m^8n^3+14ab^4m^8n^5-4ab^2m^8n^7-3am^8n^9+b^9m^9+3b^8m^9n-8b^6m^9n^3-6b^5m^9n^4+6b^4m^9n^5+8b^3m^9n^6-3bm^9n^8-m^9n^9=0\)

\(k=10\)时

\(a^{12}n^{12}-6a^{10}b^2m^2n^{10}+6a^{10}m^2n^{12}+15a^8b^4m^4n^8+14a^8b^2m^4n^{10}-29a^8m^4n^{12}-20a^6b^6m^6n^6-20a^6b^4m^6n^8+4a^6b^2m^6n^{10}+36a^6m^6n^{12}+15a^4b^8m^8n^4-20a^4b^6m^8n^6+50a^4b^4m^8n^8-36a^4b^2m^8n^{10}-9a^4m^8n^{12}-6a^2b^{10}m^{10}n^2+14a^2b^8m^{10}n^4+4a^2b^6m^{10}n^6-36a^2b^4m^{10}n^8+34a^2b^2m^{10}n^{10}-10a^2m^{10}n^{12}+b^{12}m^{12}+6b^{10}m^{12}n^2-29b^8m^{12}n^4+36b^6m^{12}n^6-9b^4m^{12}n^8-10b^2m^{12}n^{10}+5m^{12}n^{12}=0\)

\(k=11\)时

a^{15}n^{15}+3a^{14}bmn^{14}-3a^{14}mn^{15}-3a^{13}b^2m^2n^{13}+6a^{13}bm^2n^{14}-3a^{13}m^2n^{15}-17a^{12}b^3m^3n^{12}-a^{12}b^2m^3n^{13}+a^{12}bm^3n^{14}+17a^{12}m^3n^{15}-3a^{11}b^4m^4n^{11}-4a^{11}b^3m^4n^{12}+14a^{11}b^2m^4n^{13}-4a^{11}bm^4n^{14}-3a^{11}m^4n^{15}+39a^{10}b^5m^5n^{10}+21a^{10}b^4m^5n^{11}-2a^{10}b^3m^5n^{12}+2a^{10}b^2m^5n^{13}-21a^{10}bm^5n^{14}-39a^{10}m^5n^{15}+25a^9b^6m^6n^9-38a^9b^5m^6n^{10}-25a^9b^4m^6n^{11}+76a^9b^3m^6n^{12}-25a^9b^2m^6n^{13}-38a^9bm^6n^{14}+25a^9m^6n^{15}-45a^8b^7m^7n^8-17a^8b^6m^7n^9-5a^8b^5m^7n^{10}-33a^8b^4m^7n^{11}+33a^8b^3m^7n^{12}+5a^8b^2m^7n^{13}+17a^8bm^7n^{14}+45a^8m^7n^{15}-45a^7b^8m^8n^7+72a^7b^7m^8n^8+20a^7b^6m^8n^9-72a^7b^5m^8n^{10}+50a^7b^4m^8n^{11}-72a^7b^3m^8n^{12}+20a^7b^2m^8n^{13}+72a^7bm^8n^{14}-45a^7m^8n^{15}+25a^6b^9m^9n^6-17a^6b^8m^9n^7+20a^6b^7m^9n^8+28a^6b^6m^9n^9-34a^6b^5m^9n^{10}+34a^6b^4m^9n^{11}-28a^6b^3m^9n^{12}-20a^6b^2m^9n^{13}+17a^6bm^9n^{14}-25a^6m^9n^{15}+39a^5b^{10}m^{10}n^5-38a^5b^9m^{10}n^6-5a^5b^8m^{10}n^7-72a^5b^7m^{10}n^8-34a^5b^6m^{10}n^9+220a^5b^5m^{10}n^{10}-34a^5b^4m^{10}n^{11}-72a^5b^3m^{10}n^{12}-5a^5b^2m^{10}n^{13}-38a^5bm^{10}n^{14}+39a^5m^{10}n^{15}-3a^4b^{11}m^{11}n^4+21a^4b^{10}m^{11}n^5-25a^4b^9m^{11}n^6-33a^4b^8m^{11}n^7+50a^4b^7m^{11}n^8+34a^4b^6m^{11}n^9-34a^4b^5m^{11}n^{10}-50a^4b^4m^{11}n^{11}+33a^4b^3m^{11}n^{12}+25a^4b^2m^{11}n^{13}-21a^4bm^{11}n^{14}+3a^4m^{11}n^{15}-17a^3b^{12}m^{12}n^3-4a^3b^{11}m^{12}n^4-2a^3b^{10}m^{12}n^5+76a^3b^9m^{12}n^6+33a^3b^8m^{12}n^7-72a^3b^7m^{12}n^8-28a^3b^6m^{12}n^9-72a^3b^5m^{12}n^{10}+33a^3b^4m^{12}n^{11}+76a^3b^3m^{12}n^{12}-2a^3b^2m^{12}n^{13}-4a^3bm^{12}n^{14}-17a^3m^{12}n^{15}-3a^2b^{13}m^{13}n^2-a^2b^{12}m^{13}n^3+14a^2b^{11}m^{13}n^4+2a^2b^{10}m^{13}n^5-25a^2b^9m^{13}n^6+5a^2b^8m^{13}n^7+20a^2b^7m^{13}n^8-20a^2b^6m^{13}n^9-5a^2b^5m^{13}n^{10}+25a^2b^4m^{13}n^{11}-2a^2b^3m^{13}n^{12}-14a^2b^2m^{13}n^{13}+a^2bm^{13}n^{14}+3a^2m^{13}n^{15}+3ab^{14}m^{14}n+6ab^{13}m^{14}n^2+ab^{12}m^{14}n^3-4ab^{11}m^{14}n^4-21ab^{10}m^{14}n^5-38ab^9m^{14}n^6+17ab^8m^{14}n^7+72ab^7m^{14}n^8+17ab^6m^{14}n^9-38ab^5m^{14}n^{10}-21ab^4m^{14}n^{11}-4ab^3m^{14}n^{12}+ab^2m^{14}n^{13}+6abm^{14}n^{14}+3am^{14}n^{15}+b^{15}m^{15}-3b^{14}m^{15}n-3b^{13}m^{15}n^2+17b^{12}m^{15}n^3-3b^{11}m^{15}n^4-39b^{10}m^{15}n^5+25b^9m^{15}n^6+45b^8m^{15}n^7-45b^7m^{15}n^8-25b^6m^{15}n^9+39b^5m^{15}n^{10}+3b^4m^{15}n^{11}-17b^3m^{15}n^{12}+3b^2m^{15}n^{13}+3bm^{15}n^{14}-m^{15}n^{15}=0

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\(k=12\)时

a^{16}n^{16}+8a^{14}b^2m^2n^{14}-8a^{14}m^2n^{16}-68a^{12}b^4m^4n^{12}+40a^{12}b^2m^4n^{14}+28a^{12}m^4n^{16}+184a^{10}b^6m^6n^{10}-72a^{10}b^4m^6n^{12}-56a^{10}b^2m^6n^{14}-56a^{10}m^6n^{16}-250a^8b^8m^8n^8+40a^8b^6m^8n^{10}+228a^8b^4m^8n^{12}-88a^8b^2m^8n^{14}+70a^8m^8n^{16}+184a^6b^{10}m^{10}n^6+40a^6b^8m^{10}n^8-400a^6b^6m^{10}n^{10}+144a^6b^4m^{10}n^{12}+88a^6b^2m^{10}n^{14}-56a^6m^{10}n^{16}-68a^4b^{12}m^{12}n^4-72a^4b^{10}m^{12}n^6+228a^4b^8m^{12}n^8+144a^4b^6m^{12}n^{10}-316a^4b^4m^{12}n^{12}+56a^4b^2m^{12}n^{14}+28a^4m^{12}n^{16}+8a^2b^{14}m^{14}n^2+40a^2b^{12}m^{14}n^4-56a^2b^{10}m^{14}n^6-88a^2b^8m^{14}n^8+88a^2b^6m^{14}n^{10}+56a^2b^4m^{14}n^{12}-40a^2b^2m^{14}n^{14}-8a^2m^{14}n^{16}+b^{16}m^{16}-8b^{14}m^{16}n^2+28b^{12}m^{16}n^4-56b^{10}m^{16}n^6+70b^8m^{16}n^8-56b^6m^{16}n^{10}+28b^4m^{16}n^{12}-8b^2m^{16}n^{14}+m^{16}n^{16}=0

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\(k=13\)时

a^{21}n^{21}-3a^{20}bmn^{20}+3a^{20}mn^{21}-6a^{19}b^2m^2n^{19}+12a^{19}bm^2n^{20}-6a^{19}m^2n^{21}+26a^{18}b^3m^3n^{18}+10a^{18}b^2m^3n^{19}-10a^{18}bm^3n^{20}-26a^{18}m^3n^{21}+9a^{17}b^4m^4n^{17}-20a^{17}b^3m^4n^{18}+22a^{17}b^2m^4n^{19}-20a^{17}bm^4n^{20}+9a^{17}m^4n^{21}-99a^{16}b^5m^5n^{16}-57a^{16}b^4m^5n^{17}+26a^{16}b^3m^5n^{18}-26a^{16}b^2m^5n^{19}+57a^{16}bm^5n^{20}+99a^{16}m^5n^{21}+24a^{15}b^6m^6n^{15}-80a^{15}b^5m^6n^{16}-40a^{15}b^4m^6n^{17}+192a^{15}b^3m^6n^{18}-40a^{15}b^2m^6n^{19}-80a^{15}bm^6n^{20}+24a^{15}m^6n^{21}+216a^{14}b^7m^7n^{14}-8a^{14}b^6m^7n^{15}+40a^{14}b^5m^7n^{16}+264a^{14}b^4m^7n^{17}-264a^{14}b^3m^7n^{18}-40a^{14}b^2m^7n^{19}+8a^{14}bm^7n^{20}-216a^{14}m^7n^{21}-126a^{13}b^8m^8n^{13}+240a^{13}b^7m^8n^{14}+104a^{13}b^6m^8n^{15}-240a^{13}b^5m^8n^{16}+44a^{13}b^4m^8n^{17}-240a^{13}b^3m^8n^{18}+104a^{13}b^2m^8n^{19}+240a^{13}bm^8n^{20}-126a^{13}m^8n^{21}-294a^{12}b^9m^9n^{12}+310a^{12}b^8m^9n^{13}-232a^{12}b^7m^9n^{14}-376a^{12}b^6m^9n^{15}+460a^{12}b^5m^9n^{16}-460a^{12}b^4m^9n^{17}+376a^{12}b^3m^9n^{18}+232a^{12}b^2m^9n^{19}-310a^{12}bm^9n^{20}+294a^{12}m^9n^{21}+252a^{11}b^{10}m^{10}n^{11}-152a^{11}b^9m^{10}n^{12}-260a^{11}b^8m^{10}n^{13}-448a^{11}b^7m^{10}n^{14}+8a^{11}b^6m^{10}n^{15}+1200a^{11}b^5m^{10}n^{16}+8a^{11}b^4m^{10}n^{17}-448a^{11}b^3m^{10}n^{18}-260a^{11}b^2m^{10}n^{19}-152a^{11}bm^{10}n^{20}+252a^{11}m^{10}n^{21}+252a^{10}b^{11}m^{11}n^{10}-516a^{10}b^{10}m^{11}n^{11}+356a^{10}b^9m^{11}n^{12}+164a^{10}b^8m^{11}n^{13}-344a^{10}b^7m^{11}n^{14}+616a^{10}b^6m^{11}n^{15}-616a^{10}b^5m^{11}n^{16}+344a^{10}b^4m^{11}n^{17}-164a^{10}b^3m^{11}n^{18}-356a^{10}b^2m^{11}n^{19}+516a^{10}bm^{11}n^{20}-252a^{10}m^{11}n^{21}-294a^9b^{12}m^{12}n^9-152a^9b^{11}m^{12}n^{10}+356a^9b^{10}m^{12}n^{11}+1032a^9b^9m^{12}n^{12}+70a^9b^8m^{12}n^{13}-880a^9b^7m^{12}n^{14}-264a^9b^6m^{12}n^{15}-880a^9b^5m^{12}n^{16}+70a^9b^4m^{12}n^{17}+1032a^9b^3m^{12}n^{18}+356a^9b^2m^{12}n^{19}-152a^9bm^{12}n^{20}-294a^9m^{12}n^{21}-126a^8b^{13}m^{13}n^8+310a^8b^{12}m^{13}n^9-260a^8b^{11}m^{13}n^{10}+164a^8b^{10}m^{13}n^{11}+70a^8b^9m^{13}n^{12}-430a^8b^8m^{13}n^{13}+360a^8b^7m^{13}n^{14}-360a^8b^6m^{13}n^{15}+430a^8b^5m^{13}n^{16}-70a^8b^4m^{13}n^{17}-164a^8b^3m^{13}n^{18}+260a^8b^2m^{13}n^{19}-310a^8bm^{13}n^{20}+126a^8m^{13}n^{21}+216a^7b^{14}m^{14}n^7+240a^7b^{13}m^{14}n^8-232a^7b^{12}m^{14}n^9-448a^7b^{11}m^{14}n^{10}-344a^7b^{10}m^{14}n^{11}-880a^7b^9m^{14}n^{12}+360a^7b^8m^{14}n^{13}+2176a^7b^7m^{14}n^{14}+360a^7b^6m^{14}n^{15}-880a^7b^5m^{14}n^{16}-344a^7b^4m^{14}n^{17}-448a^7b^3m^{14}n^{18}-232a^7b^2m^{14}n^{19}+240a^7bm^{14}n^{20}+216a^7m^{14}n^{21}+24a^6b^{15}m^{15}n^6-8a^6b^{14}m^{15}n^7+104a^6b^{13}m^{15}n^8-376a^6b^{12}m^{15}n^9+8a^6b^{11}m^{15}n^{10}+616a^6b^{10}m^{15}n^{11}-264a^6b^9m^{15}n^{12}-360a^6b^8m^{15}n^{13}+360a^6b^7m^{15}n^{14}+264a^6b^6m^{15}n^{15}-616a^6b^5m^{15}n^{16}-8a^6b^4m^{15}n^{17}+376a^6b^3m^{15}n^{18}-104a^6b^2m^{15}n^{19}+8a^6bm^{15}n^{20}-24a^6m^{15}n^{21}-99a^5b^{16}m^{16}n^5-80a^5b^{15}m^{16}n^6+40a^5b^{14}m^{16}n^7-240a^5b^{13}m^{16}n^8+460a^5b^{12}m^{16}n^9+1200a^5b^{11}m^{16}n^{10}-616a^5b^{10}m^{16}n^{11}-880a^5b^9m^{16}n^{12}+430a^5b^8m^{16}n^{13}-880a^5b^7m^{16}n^{14}-616a^5b^6m^{16}n^{15}+1200a^5b^5m^{16}n^{16}+460a^5b^4m^{16}n^{17}-240a^5b^3m^{16}n^{18}+40a^5b^2m^{16}n^{19}-80a^5bm^{16}n^{20}-99a^5m^{16}n^{21}+9a^4b^{17}m^{17}n^4-57a^4b^{16}m^{17}n^5-40a^4b^{15}m^{17}n^6+264a^4b^{14}m^{17}n^7+44a^4b^{13}m^{17}n^8-460a^4b^{12}m^{17}n^9+8a^4b^{11}m^{17}n^{10}+344a^4b^{10}m^{17}n^{11}+70a^4b^9m^{17}n^{12}-70a^4b^8m^{17}n^{13}-344a^4b^7m^{17}n^{14}-8a^4b^6m^{17}n^{15}+460a^4b^5m^{17}n^{16}-44a^4b^4m^{17}n^{17}-264a^4b^3m^{17}n^{18}+40a^4b^2m^{17}n^{19}+57a^4bm^{17}n^{20}-9a^4m^{17}n^{21}+26a^3b^{18}m^{18}n^3-20a^3b^{17}m^{18}n^4+26a^3b^{16}m^{18}n^5+192a^3b^{15}m^{18}n^6-264a^3b^{14}m^{18}n^7-240a^3b^{13}m^{18}n^8+376a^3b^{12}m^{18}n^9-448a^3b^{11}m^{18}n^{10}-164a^3b^{10}m^{18}n^{11}+1032a^3b^9m^{18}n^{12}-164a^3b^8m^{18}n^{13}-448a^3b^7m^{18}n^{14}+376a^3b^6m^{18}n^{15}-240a^3b^5m^{18}n^{16}-264a^3b^4m^{18}n^{17}+192a^3b^3m^{18}n^{18}+26a^3b^2m^{18}n^{19}-20a^3bm^{18}n^{20}+26a^3m^{18}n^{21}-6a^2b^{19}m^{19}n^2+10a^2b^{18}m^{19}n^3+22a^2b^{17}m^{19}n^4-26a^2b^{16}m^{19}n^5-40a^2b^{15}m^{19}n^6-40a^2b^{14}m^{19}n^7+104a^2b^{13}m^{19}n^8+232a^2b^{12}m^{19}n^9-260a^2b^{11}m^{19}n^{10}-356a^2b^{10}m^{19}n^{11}+356a^2b^9m^{19}n^{12}+260a^2b^8m^{19}n^{13}-232a^2b^7m^{19}n^{14}-104a^2b^6m^{19}n^{15}+40a^2b^5m^{19}n^{16}+40a^2b^4m^{19}n^{17}+26a^2b^3m^{19}n^{18}-22a^2b^2m^{19}n^{19}-10a^2bm^{19}n^{20}+6a^2m^{19}n^{21}-3ab^{20}m^{20}n+12ab^{19}m^{20}n^2-10ab^{18}m^{20}n^3-20ab^{17}m^{20}n^4+57ab^{16}m^{20}n^5-80ab^{15}m^{20}n^6+8ab^{14}m^{20}n^7+240ab^{13}m^{20}n^8-310ab^{12}m^{20}n^9-152ab^{11}m^{20}n^{10}+516ab^{10}m^{20}n^{11}-152ab^9m^{20}n^{12}-310ab^8m^{20}n^{13}+240ab^7m^{20}n^{14}+8ab^6m^{20}n^{15}-80ab^5m^{20}n^{16}+57ab^4m^{20}n^{17}-20ab^3m^{20}n^{18}-10ab^2m^{20}n^{19}+12abm^{20}n^{20}-3am^{20}n^{21}+b^{21}m^{21}+3b^{20}m^{21}n-6b^{19}m^{21}n^2-26b^{18}m^{21}n^3+9b^{17}m^{21}n^4+99b^{16}m^{21}n^5+24b^{15}m^{21}n^6-216b^{14}m^{21}n^7-126b^{13}m^{21}n^8+294b^{12}m^{21}n^9+252b^{11}m^{21}n^{10}-252b^{10}m^{21}n^{11}-294b^9m^{21}n^{12}+126b^8m^{21}n^{13}+216b^7m^{21}n^{14}-24b^6m^{21}n^{15}-99b^5m^{21}n^{16}-9b^4m^{21}n^{17}+26b^3m^{21}n^{18}+6b^2m^{21}n^{19}-3bm^{21}n^{20}-m^{21}n^{21}=0

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mathe · 发表于 2014-4-30 08:32:03

8楼红色公式一般情况不成立，但是俩椭圆中心重合时正好符合，所以18#结果能符合，但是前面一些数据应该不对

数学星空 · 发表于 2014-4-30 20:22:44

找到了mathe提供的椭圆曲线理论的相关结论：

数学星空 · 发表于 2014-4-30 21:12:27

对于13#结果与下面是椭圆曲线理论算出的结果一致，下面是椭圆曲线理论算出的结果：\( k=3 \sim 13\)，

当\(k=3\)时

\(-4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^2m^2-(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2＝0\)

当\(k=4\)时

\(8a^2b^2n^4m^4+4n^2m^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)+(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3＝0\)

当\(k=5\)时

\(256a^4b^4n^8m^8+(128(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^2b^2m^6n^6+32n^4m^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^2b^2-64m^6n^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3-48n^4m^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2-12n^2m^2(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)-(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6＝0\)

当\(k=6\)时

\(3(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6+20n^2m^2(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)+96n^4m^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^2b^2+16n^4m^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2+(384(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^2b^2m^6n^6-64m^6n^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3+512a^4b^4n^8m^8=0\)

当\(k=7\)时

\(65536a^8b^8n^{16}m^{16}+(98304(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{14}m^{14}a^6b^6+24576(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^6b^6n^{12}m^{12}+16384(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{14}m^{14}a^4b^4+61440(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{12}m^{12}a^4b^4+27648(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{10}m^{10}a^4b^4+3328(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6a^4b^4n^8m^8+(8192(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{12}m^{12}a^2b^2+16384(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{10}m^{10}a^2b^2+9216(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^8m^8a^2b^2+2048(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^6m^6a^2b^2+160(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9a^2b^2n^4m^4-4096(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{12}m^{12}-6144(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{10}m^{10}-3840(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^8m^8-1280(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^6m^6-240(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^4m^4-24(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^2m^2-(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}=0\)

当\(k=8\)时

\(-(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}-16(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^2m^2-80(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9a^2b^2n^4m^4-80(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^4m^4-1280(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^6m^6a^2b^2-7680(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^8m^8a^2b^2+1280(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^8m^8-2048(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{10}m^{10}a^4b^4-20480(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{10}m^{10}a^2b^2+4096(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{10}m^{10}+8192(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^6b^6n^{12}m^{12}-16384(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{12}m^{12}a^4b^4-(20480(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{12}m^{12}a^2b^2+4096(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{12}m^{12}+(32768(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{14}m^{14}a^6b^6-32768(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{14}m^{14}a^4b^4+32768a^8b^8n^{16}m^{16}＝0\)

当\(k=9\)时

25165824(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^{10}b^{10}n^{20}m^{20}-16777216(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{22}m^{22}a^8b^8+3145728(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{20}m^{20}a^4b^4+4718592(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6a^8b^8n^{16}m^{16}+19200(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}a^4b^4n^8m^8+417792(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9a^6b^6n^{12}m^{12}+480(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}a^2b^2n^4m^4+50331648a^{12}b^{12}n^{24}m^{24}-36(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^2m^2-5376(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^6m^6-129024(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{10}m^{10}-589824(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7n^{14}m^{14}-576(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^4m^4-32256(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^8m^8-344064(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{12}m^{12}-589824(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8n^{16}m^{16}-262144(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9n^{18}m^{18}-(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{18}+378880(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{10}m^{10}a^2b^2+4718592(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{14}m^{14}a^6b^6+3342336(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{14}m^{14}a^4b^4+1802240(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{14}m^{14}a^2b^2+36700160(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{18}m^{18}a^8b^8+12582912(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{18}m^{18}a^6b^6+83456(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^8m^8a^2b^2-1572864(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{18}m^{18}a^4b^4+67108864(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{20}m^{20}a^8b^8+1560576(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{12}m^{12}a^4b^4+1024000(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{12}m^{12}a^2b^2+16515072(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{16}m^{16}a^6b^6+1376256(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{16}m^{16}a^4b^4+2228224(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{16}m^{16}a^2b^2+9856(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^6m^6a^2b^2+288768(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{10}m^{10}a^4b^4+(100663296(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{22}m^{22}a^{10}b^{10}+(1572864(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7n^{18}m^{18}a^2b^2-(18874368(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{20}m^{20}a^6b^6＝0

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当\(k=10\)时

10485760(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^{10}b^{10}n^{20}m^{20}+20971520(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{22}m^{22}a^8b^8-5242880(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{20}m^{20}a^4b^4+2949120(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6a^8b^8n^{16}m^{16}+35584(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}a^4b^4n^8m^8+450560(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9a^6b^6n^{12}m^{12}+1152(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}a^2b^2n^4m^4+16777216a^{12}b^{12}n^{24}m^{24}+100(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^2m^2-1792(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^6m^6-215040(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{10}m^{10}-720896(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7n^{14}m^{14}+576(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^4m^4-39424(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^8m^8-573440(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{12}m^{12}-196608(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8n^{16}m^{16}+262144(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9n^{18}m^{18}+5(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{18}+901120(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{10}m^{10}a^2b^2+5898240(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{14}m^{14}a^6b^6+14090240(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{14}m^{14}a^4b^4+524288(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{14}m^{14}a^2b^2+24903680(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{18}m^{18}a^8b^8+52428800(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3n^{18}m^{18}a^6b^6+210944(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^8m^8a^2b^2+8912896(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5n^{18}m^{18}a^4b^4+57671680(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{20}m^{20}a^8b^8+4280320(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{12}m^{12}a^4b^4+1802240(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{12}m^{12}a^2b^2+27525120(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2n^{16}m^{16}a^6b^6+21299200(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{16}m^{16}a^4b^4-3670016(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6n^{16}m^{16}a^2b^2+24576(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^6m^6a^2b^2+624640(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{10}m^{10}a^4b^4+(41943040(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)n^{22}m^{22}a^{10}b^{10}-(4194304(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7n^{18}m^{18}a^2b^2+(31457280(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2))(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4n^{20}m^{20}a^6b^6=0

复制代码

当\(k=11\)时

-75520m^8n^8(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{24}a^4b^4-1120m^4n^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{27}a^2b^2-89980928m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{18}a^8b^8-3817472m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{21}a^6b^6-12884901888m^32n^32(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{12}a^4b^4+13421772800m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9a^{14}b^{14}+755914244096m^36n^36(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^{12}b^{12}-4244635648m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}a^{12}b^{12}-998244352m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}a^{10}b^{10}+824633720832m^36n^36(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^{18}b^{18}+214748364800m^32n^32(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6a^{16}b^{16}-2748779069440m^38n^38(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^{16}b^{16}-17179869184m^34n^34(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9a^8b^8+1099511627776m^40n^40a^{20}b^{20}+7046430720m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{13}+4026531840m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{14}+7633633280m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{12}+3148873728m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{10}+421724160m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8+20500480m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{18}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6+349440m^8n^8(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{22}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4+1680m^4n^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{26}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2+5725224960m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{11}+1312030720m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9+105431040m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7+3075072m^{10}n^{10}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{20}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5+29120m^6n^6(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{24}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3+60m^2n^2(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{28}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)+1073741824m^{30}n^{30}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{15}+(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{30}-233963520m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{18}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^4b^4-2408448m^{10}n^{10}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{22}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^4b^4-6442450944m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{13}a^2b^2-50734301184m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{11}a^2b^2-30744248320m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9a^2b^2-5064622080m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^2b^2-343572480m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{17}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^2b^2-8474624m^{10}n^{10}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{21}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^2b^2-43904m^6n^6(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{25}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^2b^2-177251287040m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^8b^8-2451832832m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^8b^8+429496729600m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9a^6b^6+386547056640m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^6b^6-76101451776m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^6b^6-10066329600m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^6b^6-114032640m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{19}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^6b^6-77309411328m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{11}a^4b^4+37580963840m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9a^4b^4+36842766336m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^4b^4-754974720m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^4b^4-4810363371520m^34n^34(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^{14}b^{14}+42949672960m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{14}b^{14}-7524782702592m^34n^34(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^{12}b^{12}-4144643440640m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^{12}b^{12}-100260642816m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{12}b^{12}+1649267441664m^34n^34(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^{10}b^{10}-5617817223168m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^{10}b^{10}-1309965025280m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^{10}b^{10}-24360517632m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{10}b^{10}+854698491904m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^8b^8-1245406298112m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^8b^8+3298534883328m^38n^38(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{18}b^{18}+1546188226560m^34n^34(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{16}b^{16}-51539607552m^32n^32(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{10}a^6b^6+724775731200m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8a^6b^6+14092861440m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^6b^6-39636172800m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^6b^6-1450967040m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{17}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^6b^6-56371445760m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{10}a^4b^4+68702699520m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8a^4b^4+7839154176m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^4b^4-875888640m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^4b^4-32514048m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{20}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^4b^4-29527900160m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{12}a^2b^2-48653926400m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{10}a^2b^2-14136901632m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8a^2b^2-1467482112m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^2b^2-62791680m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{19}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^2b^2-783360m^8n^8(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{23}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^2b^2+2061584302080m^36n^36(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^{16}b^{16}-7559142440960m^36n^36(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^{14}b^{14}-773094113280m^32n^32(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^{14}b^{14}-9083855831040m^32n^32(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^{12}b^{12}-922075791360m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^{12}b^{12}-2439541424128m^32n^32(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^{10}b^{10}-3833258311680m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^{10}b^{10}-246021095424m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^{10}b^{10}+1352914698240m^32n^32(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8a^8b^8-877247070208m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^8b^8-638977048576m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^8b^8-28273803264m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^8b^8=0

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当\(k=12\)时

28160m^8n^8(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{18}a^4b^4-352m^4n^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{21}a^2b^2+178257920m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9a^{10}b^{10}+2684354560m^{28}n^{28}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^8b^8+15073280m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}a^8b^8+917504m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}a^6b^6+5368709120m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3a^{14}b^{14}+1342177280m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6a^{12}b^{12}-4294967296m^{30}n^{30}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^{12}b^{12}-671088640m^{26}n^{26}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9a^4b^4+54067200m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8+3784704m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6+42240m^8n^8(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4-352m^4n^4(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{20}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2+8589934592m^32n^32a^{16}b^{16}+161480704m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{10}+134217728m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{11}+115343360m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9+17301504m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7+540672m^{10}n^{10}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5-32m^2n^2(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{22}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)+50331648m^{24}n^{24}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{12}-(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{24}+743424m^{10}n^{10}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{16}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^4b^4-922746880m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^9a^2b^2-692060160m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^2b^2-90832896m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^2b^2-2703360m^{10}n^{10}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{15}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^2b^2-14080m^6n^6(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{19}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^2b^2+6979321856m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^{10}b^{10}+2046820352m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{10}b^{10}+1610612736m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^8b^8+3623878656m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^8b^8+236978176m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^8b^8+2684354560m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^6b^6+4127195136m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^6b^6+828375040m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^6b^6+19529728m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^6b^6-100663296m^{22}n^{22}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^7a^4b^4+445644800m^{18}n^{18}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^5a^4b^4+53084160m^{14}n^{14}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{12}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^3a^4b^4+21474836480m^{30}n^{30}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{14}b^{14}+10468982784m^{26}n^{26}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)a^{12}b^{12}-253440m^8n^8(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{17}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^2b^2+19327352832m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^{12}b^{12}-5905580032m^{28}n^{28}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^{10}b^{10}+7449083904m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^{10}b^{10}+3791650816m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^4(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^8b^8+1390411776m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^8(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^8b^8+4563402752m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^3(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^6b^6+2348810240m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^7(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^6b^6+173015040m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{11}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^6b^6-838860800m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^2(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8a^4b^4+478150656m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^6(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^4b^4+200540160m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{10}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^4b^4+8421376m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{14}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^2a^4b^4-369098752m^{24}n^{24}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^{10}a^2b^2-1038090240m^{20}n^{20}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^5(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^8a^2b^2-302776320m^{16}n^{16}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^9(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^6a^2b^2-18923520m^{12}n^{12}(a^2n^2+b^2m^2+m^2n^2-m^2y_0^2-n^2x_0^2)^{13}(-a^2b^2-a^2n^2+a^2y_0^2-b^2m^2+b^2x_0^2)^4a^2b^2=0

复制代码

当\(k=13\)时

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经mathe提醒，我重新按照另一种方法：即下面的递推式计算发现，上面的结果是错误，特此说明；
正确的结果见楼下说明

数学星空 · 发表于 2014-5-2 12:54:22

其实，我们可以有更简单的计算方法：按照mathe的方案，我们直接利用递推式确定\(\psi[n]\)即可

\(A=\frac{(-u_2^2+3u_1)}{3u_0^2}, B=\frac{(2u_2^3-9u_1u_2+27u_0)}{27u_0^3}, x=\frac{u_2}{3u_0}, y=\frac{1}{u_0}\)

\(\psi[0] =0\)

\(\psi[1] =1\)

\(\psi[2] =\frac{2}{u_0}\)

\(\psi[3] =\frac{4u_0u_2-u_1^2}{u_0^4}\)

\(\psi[4] =-\frac{4(-4u_0u_1u_2+u_1^3+8u_0^2)}{u_0^7}\)

\(\psi[2k] = \frac{u_0\psi[k](-\psi[k-2]\psi[k+1]^2+\psi[k-1]^2\psi[k+2])}{2}\)

\(\psi[2k+1] = \psi[k]^3\psi[k+2]-\psi[k-1]\psi[k+1]^3\)

数学星空 · 发表于 2014-5-2 14:11:06

通过计算，我们可以得到双椭圆心距公式：

外椭圆 \(\frac{(x-x_0)^2}{m^2}+\frac{(y-y_0)^2}{n^2}=1\),内椭圆： \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

我们设

\(\frac{x_0^2}{m^2}+\frac{y_0^2}{n^2}=R^2\)

\(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}=r^2\)

当\(n=3\)时

\(-4m^2n^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)-(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2=0\)

当\(n=4\)时

\(-32m^4n^4a^2b^2-16m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)-4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3=0\)

当\(n=5\)时

\(-256m^8n^8a^4b^4-128m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2-32m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^2b^2+64m^6n^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3+48m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2+12m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)+(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6=0\)

当\(n=6\)时

\(512m^8n^8a^4b^4+384m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2+96m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^2b^2-64m^6n^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3+16m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2+20m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)+3(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6=0\)

当\(n=7\)时

\(65536m^{16}n^{16}a^8b^8+98304m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^6b^6+24576m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^6b^6+16384m^{14}n^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^4b^4+61440m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^4b^4+27648m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^4b^4+3328m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6a^4b^4+8192m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^2b^2+16384m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^2b^2+9216m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^2b^2+2048m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2+160m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9a^2b^2-4096m^{12}n^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6-6144m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5-3840m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4-1280m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3-240m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2-24m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)-(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}=0\)

当\(n=8\)时

\(32768m^{16}n^{16}a^8b^8+32768m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^6b^6+8192m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^6b^6-32768m^{14}n^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^4b^4-16384m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^4b^4-2048m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^4b^4-20480m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^2b^2-20480m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^2b^2-7680m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^2b^2-1280m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2-80m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9a^2b^2+4096m^{12}n^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6+4096m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5+1280m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4-80m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2-16m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)-(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}=0\)

当\(n=9\)时

4718592m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6a^8b^8+417792m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9a^6b^6+3145728m^{20}n^{20}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^4b^4+19200m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}a^4b^4+480m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}a^2b^2+25165824m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^{10}b^{10}-16777216m^{22}n^{22}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^8b^8-262144m^{18}n^{18}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9+67108864m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^8b^8-18874368m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^6b^6+16515072m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^6b^6+1376256m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^4b^4+1560576m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^4b^4+2228224m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^2b^2+36700160m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^8b^8+12582912m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^6b^6+4718592m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^6b^6-1572864m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^4b^4+3342336m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^4b^4+288768m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^4b^4+1572864m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^2b^2+1802240m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^2b^2+378880m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^2b^2+9856m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2+100663296m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{10}b^{10}+1024000m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^2b^2+83456m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^2b^2-(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{18}-589824m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8-344064m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6-32256m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4-576m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2-589824m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7-129024m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5-5376m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3-36m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)+50331648m^{24}n^{24}a^{12}b^{12}=0

复制代码

当\(n=10\)时

2949120m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6a^8b^8+450560m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9a^6b^6-5242880m^{20}n^{20}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^4b^4+35584m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}a^4b^4+1152m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}a^2b^2+10485760m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^{10}b^{10}+20971520m^{22}n^{22}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^8b^8+262144m^{18}n^{18}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9+57671680m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^8b^8+31457280m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^6b^6+27525120m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^6b^6+21299200m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^4b^4+4280320m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^4b^4-3670016m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^2b^2+24903680m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^8b^8+52428800m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^6b^6+5898240m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^6b^6+8912896m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^4b^4+14090240m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^4b^4+624640m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^4b^4-4194304m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^2b^2+524288m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^2b^2+901120m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^2b^2+24576m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2+41943040m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{10}b^{10}+1802240m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^2b^2+210944m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^2b^2+5(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{18}-196608m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8-573440m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6-39424m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4+576m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2-720896m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7-215040m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5-1792m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3+100m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)+16777216m^{24}n^{24}a^{12}b^{12}=0

复制代码

当\(n=11\)时

-824633720832m^36n^36(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^{18}b^{18}-214748364800m^{32}n^{32}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6a^{16}b^{16}-13421772800m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9a^{14}b^{14}-755914244096m^36n^36(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^{12}b^{12}+4244635648m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}a^{12}b^{12}+998244352m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}a^{10}b^{10}+2748779069440m^38n^38(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^{16}b^{16}+17179869184m^34n^34(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9a^8b^8+89980928m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{18}a^8b^8+3817472m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{21}a^6b^6+12884901888m^{32}n^{32}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{12}a^4b^4+75520m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{24}a^4b^4+1120m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{27}a^2b^2-1073741824m^{30}n^{30}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{15}-3298534883328m^38n^38(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{18}b^{18}-1546188226560m^34n^34(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{16}b^{16}+4810363371520m^34n^34(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^{14}b^{14}-42949672960m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{14}b^{14}+7524782702592m^34n^34(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^{12}b^{12}+4144643440640m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^{12}b^{12}+100260642816m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{12}b^{12}-1649267441664m^34n^34(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^{10}b^{10}+5617817223168m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^{10}b^{10}+1309965025280m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^{10}b^{10}+24360517632m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{10}b^{10}-854698491904m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^8b^8+1245406298112m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^8b^8+177251287040m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^8b^8+32514048m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{20}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^4b^4+29527900160m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{12}a^2b^2+48653926400m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{10}a^2b^2+14136901632m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8a^2b^2+1467482112m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^2b^2+62791680m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{19}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^2b^2+783360m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{23}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^2b^2+2451832832m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^8b^8-429496729600m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9a^6b^6-386547056640m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^6b^6+76101451776m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^6b^6+10066329600m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^6b^6+114032640m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{19}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^6b^6+77309411328m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{11}a^4b^4-37580963840m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9a^4b^4-36842766336m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^4b^4+754974720m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^4b^4+233963520m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{18}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^4b^4+2408448m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{22}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^4b^4+6442450944m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{13}a^2b^2+50734301184m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{11}a^2b^2+30744248320m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9a^2b^2+5064622080m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^2b^2+343572480m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{17}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^2b^2+8474624m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{21}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^2b^2+43904m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{25}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2-2061584302080m^36n^36(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^{16}b^{16}+7559142440960m^36n^36(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^{14}b^{14}+773094113280m^{32}n^{32}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^{14}b^{14}+9083855831040m^{32}n^{32}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^{12}b^{12}+922075791360m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^{12}b^{12}+2439541424128m^{32}n^{32}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^{10}b^{10}+3833258311680m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^{10}b^{10}+246021095424m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^{10}b^{10}-1352914698240m^{32}n^{32}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8a^8b^8+877247070208m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^8b^8+638977048576m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^8b^8+28273803264m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^8b^8+51539607552m^{32}n^{32}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{10}a^6b^6-724775731200m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8a^6b^6-14092861440m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^6b^6+39636172800m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^6b^6+1450967040m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{17}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^6b^6+56371445760m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{10}a^4b^4-68702699520m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8a^4b^4-7839154176m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^4b^4+875888640m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^4b^4-(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{30}-5725224960m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{11}-1312030720m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9-105431040m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7-3075072m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{20}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5-29120m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{24}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3-60m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{28}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)-7046430720m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{13}-4026531840m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{14}-7633633280m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{12}-3148873728m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{10}-421724160m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8-20500480m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{18}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6-349440m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{22}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4-1680m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{26}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2-1099511627776m^40n^40a^{20}b^{20}=0

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当\(n=12\)时

5368709120m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3a^{14}b^{14}+1342177280m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6a^{12}b^{12}+178257920m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9a^{10}b^{10}+2684354560m^{28}n^{28}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^8b^8+15073280m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}a^8b^8+917504m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}a^6b^6+28160m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{18}a^4b^4-352m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{21}a^2b^2-4294967296m^{30}n^{30}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^{12}b^{12}-671088640m^{26}n^{26}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9a^4b^4+50331648m^{24}n^{24}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{12}+19327352832m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^{12}b^{12}-5905580032m^{28}n^{28}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^{10}b^{10}+7449083904m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^{10}b^{10}+3791650816m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^8b^8+1390411776m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^8b^8+4563402752m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^6b^6+2348810240m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^6b^6+173015040m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^6b^6-838860800m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8a^4b^4+478150656m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^4b^4+200540160m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^4b^4+8421376m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^4b^4-369098752m^{24}n^{24}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{10}a^2b^2-1038090240m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8a^2b^2-302776320m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6a^2b^2-18923520m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4a^2b^2-253440m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{17}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2a^2b^2+21474836480m^{30}n^{30}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{14}b^{14}+10468982784m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{12}b^{12}+6979321856m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^{10}b^{10}+2046820352m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^{10}b^{10}+1610612736m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^8b^8+3623878656m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^8b^8+236978176m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^8b^8+2684354560m^{26}n^{26}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^6b^6+4127195136m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^5(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^6b^6+828375040m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^9(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^6b^6+19529728m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{13}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^6b^6-100663296m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^4b^4+445644800m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^4b^4+53084160m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^4b^4+743424m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^4b^4-922746880m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^3(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9a^2b^2-692060160m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^7(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7a^2b^2-90832896m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{11}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5a^2b^2-2703360m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{15}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^3a^2b^2-14080m^6n^6(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{19}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)a^2b^2-(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{24}+8589934592m^{32}n^{32}a^{16}b^{16}+134217728m^{22}n^{22}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^2(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{11}+115343360m^{18}n^{18}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^6(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^9+17301504m^{14}n^{14}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{10}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^7+540672m^{10}n^{10}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{14}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^5-32m^2n^2(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{22}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)+161480704m^{20}n^{20}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^4(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^{10}+54067200m^{16}n^{16}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^8(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^8+3784704m^{12}n^{12}(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{12}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^6+42240m^8n^8(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{16}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^4-352m^4n^4(-R^2m^2n^2+a^2n^2+b^2m^2+m^2n^2)^{20}(a^2b^2r^2-a^2b^2-a^2n^2-b^2m^2)^2=0

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当\(n=13\)时

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当\(n=14\)时

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[讨论] 双椭圆外切内接N边形问题

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