A^4 + B^4 + C^4 = D^4的正整数解
关于这个方程$A^4 + B^4 + C^4 = D^4$的正整数解,可否在计算上打破他们在2008年的记录 https://euler413.narod.ru/
https://oeis.org/A003828
N A B C D Autor
1 422481 414560 217519 95800 (Roger Frye, 1988)
2 2813001 2767624 1390400 673865 (Allan MacLeod 1997)
3 8707481 8332208 5507880 1705575 (D.J. Bernstein, 2001)
4 12197457 11289040 8282543 5870000 (D.J. Bernstein, 2001)
5 16003017 14173720 12552200 4479031 (D.J. Bernstein, 2001)
6 16430513 16281009 7028600 3642840 (D.J. Bernstein, 2001)
7 20615673 18796760 15365639 2682440 (Noam Elkies, 1986)
8 44310257 41084175 31669120 2164632 (Robert Gerbicz, 11/08/2006)
9 68711097 65932985 42878560 10409096 (Robert Gerbicz, 11/08/2006)
10 117112081 106161120 87865617 34918520 (Robert Gerbicz, 11/02/2006)
11 145087793 122055375 121952168 1841160 (Juergen Rathmann, 5/31/2007)
12 156646737 146627384 108644015 27450160 (Juergen Rathmann, 6/1/2007)
13 589845921 582665296 260052385 186668000 (Seiji Tomita, 03/13/2006)
14 638523249 630662624 275156240 219076465 (Allan MacLeod,1998)
15 873822121 769321280 606710871 558424440 (Robert Gerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 11/2/2007)
16 1259768473 1166705840 859396455 588903336 (Robert Gerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 01/25/2008)
17 1679142729 1670617271 632671960 50237800 (Seiji Tomita, 03/13/2006)
18 1787882337 1662997663 1237796960 686398000 (Robert Gerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 11/2/2007)
19 1871713857 1593513080 1553556440 92622401 (Robert Gerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 10/31/2007)
20 3393603777 3134081336 2448718655 664793200 (Seiji Tomita, 01/28/2007)
21 15434547801 15355831360 5821981400 140976551 (Seiji Tomita, 10/24/2007)
22 5062297699257 4987588419655 2480452675600 502038853976 (Seiji Tomita, 05/15/2008)
23 29999857938609 27239791692640 22495595284040 7592431981391 (Seiji Tomita, 03/13/2006)
24 573646321871961 514818101299289 440804942580160 130064300991400 (Seiji Tomita, 09/15/2008)
25 20249506709579721 18565945114216720 14890026433468471 3579087147375440 (Seiji Tomita, 08/13/2008)
26 62940516903410601 56827813308111785 47886740272114976 8813425670440240 (Seiji Tomita, 08/13/2008)
27 1677479490238223823661446513 1507524066882038472584786800 1288056982586427591062203384 169218021322170204480680305 (Seiji Tomita, 03/13/2006) NEW!
9033964577482532388059482429398457291004947925005743028147465732645880^4 +
4417264698994538496943597489754952845854672497179047898864124209346920^4 +
1439965710648954492268506771833175267850201426615300442218292336336633^4 =
9161781830035436847832452398267266038227002962257243662070370888722169^4 (M.A.FAJJAL, 5/31/2009) 这些记录应该都是大型机或者分布式运算得到的吧？打破纪录难度比较大，就看你的了:hug: http://www.maroon.dti.ne.jp/fermat/dioph46e.html
http://www.maroon.dti.ne.jp/fermat/grouplaw1e.html A274015
Least number of the form x^2 + y^4 in exactly n ways where x and y are nonzero integers.
2, 17, 3026, 141457, 4740625, 113260225, 205117028945, 3234825286225 3234825286225 = 1235^4+ 953160^2
=780^4+ 1692535^2
=637^4+ 1752192^2
=416^4+ 1790217^2
=195^4+ 1798160^2
= 1092^4+ 1346423^2
= 1341^4+ 31792^2
=979^4+ 1521912^2 northwolves 发表于 2025-5-24 21:17
NEW!
怎么得到的？ 这个除了硬搜两数四次方和和四次方差有其它技巧吗？ NA B C D Autor
1422481 414560 217519 95800 (Roger Frye, 1988)
22813001 2767624 1390400 673865 (Allan MacLeod 1997)
38707481 8332208 5507880 1705575 (D.J. Bernstein, 2001)
412197457 11289040 8282543 5870000 (D.J. Bernstein, 2001)
516003017 14173720 12552200 4479031 (D.J. Bernstein, 2001)
616430513 16281009 7028600 3642840 (D.J. Bernstein, 2001)
720615673 18796760 15365639 2682440 (Noam Elkies, 1986)
844310257 41084175 31669120 2164632 (RobertGerbicz, 11/08/2006)
968711097 65932985 42878560 10409096 (RobertGerbicz, 11/08/2006)
10 117112081 106161120 87865617 34918520 (RobertGerbicz, 11/02/2006)
11 145087793 122055375 121952168 1841160 (Juergen Rathmann, 5/31/2007)
12 156646737 146627384 108644015 27450160 (Juergen Rathmann, 6/1/2007)
13 589845921 582665296 260052385 186668000 (Seiji Tomita, 03/13/2006)
14 638523249 630662624 275156240 219076465 (Allan MacLeod,1998)
15 873822121 769321280 606710871 558424440 (RobertGerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 11/2/2007)
16 1259768473 1166705840 859396455 588903336 (RobertGerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 01/25/2008)
17 1679142729 1670617271 632671960 50237800 (Seiji Tomita, 03/13/2006)
18 1787882337 1662997663 1237796960 686398000 (RobertGerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 11/2/2007)
19 1871713857 1593513080 1553556440 92622401 (RobertGerbicz, Leonid Durman,Yuri Radaev, Alexey Zubkov 10/31/2007)
20 3393603777 3134081336 2448718655 664793200 (Seiji Tomita, 01/28/2007)
21 15434547801 15355831360 5821981400 140976551 (Seiji Tomita, 10/24/2007)
22 5062297699257 4987588419655 2480452675600 502038853976 (Seiji Tomita, 05/15/2008)
23 29999857938609 27239791692640 22495595284040 7592431981391 (Seiji Tomita, 03/13/2006)
24 573646321871961 514818101299289 440804942580160 130064300991400 (Seiji Tomita, 09/15/2008)
25 20249506709579721 18565945114216720 14890026433468471 3579087147375440 (Seiji Tomita, 08/13/2008)
26 62940516903410601 56827813308111785 47886740272114976 8813425670440240 (Seiji Tomita, 08/13/2008)
27 1677479490238223823661446513 1507524066882038472584786800 1288056982586427591062203384 169218021322170204480680305 (Seiji Tomita, 03/13/2006)
弄文本处理工具，帮你对齐一下 无意间搜到了这个帖子, 内有乾坤, 记录已经被2024年stackexchange的一些人给打破了.
https://math.stackexchange.com/questions/1853223/distribution-of-primitive-pythagorean-triples-ppt-and-of-solutions-of-a4b4/4857107#4857107
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