(k1)^3+(k2)^3+(k3)^3=n^3

王守恩 · 发表于 2025-12-17 09:44:52

lsr314 发表于 2018-9-11 09:12
这里a可以约掉了，能找到互素的吗？

互素解。

$0^3=1^3-1^3-0^3$

$1^3=9^3-6^3-8^3$

$2^3=41^3-17^3-40^3$

$3^3=115^3-34^3-114^3$

$4^3=249^3-57^3-248^3$

$5^3=461^3-86^3-460^3$

$6^3=769^3-121^3-768^3$

$7^3=1191^3-162^3-1190^3$

$8^3=1745^3-209^3-1744^3$

$9^3=2449^3-262^3-2448^3$

$10^3=3321^3-321^3-3320^3$

$11^3=4379^3-386^3-4378^3$

$12^3=5641^3-457^3-5640^3$

$13^3=7125^3-534^3-7124^3$

$14^3=8849^3-617^3-8848^3$

$\cdots\cdots$

把中间的数提出来——1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321, 386, 457, 534, 617, 706, 801, 902, 1009, 1122, 1241, 1366, 1497, 1634, 1777, 1926, 2081, 2242, 2409, 2582, 2761, 2946,——A056109——没有这条文。

$0^3=-1^3+1^3-0^3$

$1^3=1^3+2^3-2^3$

$2^3=15^3+9^3-16^3$

$3^3=59^3+22^3-60^3$

$4^3=151^3+41^3-152^3$

$5^3=309^3+66^3-310^3$

$6^3=551^3+97^3-552^3$

$7^3=895^3+134^3-896^3$

$8^3=1359^3+177^3-1360^3$

$9^3=1961^3+226^3-1962^3$

$10^3=2719^3+281^3-2720^3$

$11^3=3651^3+342^3-3652^3$

$12^3=4775^3+409^3-4776^3$

$13^3=6109^3+482^3-6110^3$

$14^3=7671^3+561^3-7672^3$

$15^3=9479^3+646^3-9480^3$

$\cdots\cdots$

把中间的数提出来——1, 2, 9, 22, 41, 66, 97, 134, 177, 226, 281, 342, 409, 482, 561, 646, 737, 834, 937, 1046, 1161, 1282, 1409, 1542, 1681, 1826, 1977, 2134, 2297, 2466, 2641, 2822,—— A056105——没有这条文

northwolves · 发表于 2025-12-17 13:31:25

王守恩发表于 2025-12-17 09:44
互素解。

$0^3=1^3-1^3-0^3$

$n^3=(3n^3+3n^2+2n+1)^3-(3n^2+2n+1)^3-(3n^3+3n^2+2n)^3$
中间的数就是$3n^2+2n+1$

王守恩 · 发表于 6 天前

$(k1)^3+(k2)^3+(k3)^3=n$没有通项公式。$(k1)^3+(k2)^3+(k3)^3+(k4)^3=n$也没有找到通项公式——参考链接:https://www.alpertron.com.ar/FCUBES.HTM

$6x=(x-1)^3+(-x)^3+(-x)^3+(x+1)^3$

$6x+3=(x)^3+(-x+4)^3+(2x-5)^3+(-2x+4)^3$

$18x+1=(2x+14)^3+(-2x-23)^3+(-3x-26)^3+(3x+30)^3$

$18x+7=(x+2)^3+(6x-1)^3+(8x-2)^3+(-9x+2)^3$

$18x+8=(x-5)^3+(-x+14)^3+(-3x+29)^3+(3x-30)^3$

$54x+20=(3x-11)^3+(-3x+10)^3+(x+2)^3+(-x+7)^3$

$72x+56=(-9x+4)^3+(x+4)^3+(6x-2)^3+(8x-4)^3$

$108x+2=(-x-22)^3+(x+4)^3+(-3x-41)^3+(3x+43)^3$

$216x+92=(3x-164)^3+(-3x+160)^3+(x-35)^3+(-x+71)^3$

$270x+146=(-60x+91)^3+(-3x+13)^3+(22x-37)^3+(59x-89)^3$

$270x+200=(3x+259)^3+(-3x-254)^3+(x+62)^3+(-x-107)^3$

$270x+218=(-3x-56)^3+(3x+31)^3+(-5x-69)^3+(5x+78)^3$

$432x+380=(-3x+64)^3+(3x-80)^3+(2x-29)^3+(-2x+65)^3$

$540x+38=(5x-285)^3+(-5x+267)^3+(3x-140)^3+(-3x+190)^3$

$810x+56=(5x-755)^3+(-5x+836)^3+(9x-1445)^3+(-9x+1420)^3$

$810x+164=(3x-26)^3+(-3x+1)^3+(5x-21)^3+(-5x+30)^3$

$1080x+380=(-x-1438)^3+(x+1258)^3+(-3x-4037)^3+(3x+4057)^3$

$1620x+1334=(-5x-3269)^3+(5x+3107)^3+(-9x-5714)^3+(9x+5764)^3$

$1620x+1352=(-5x+434)^3+(5x-353)^3+(9x-722)^3+(-9x+697)^3$

$2160x+362=(-5x-180)^3+(5x+108)^3+(-6x-149)^3+(6x+199)^3$

$6480x+794=(-5x-83)^3+(5x+11)^3+(-6x-35)^3+(6x+85)^3$

If n = 596, 1892, 2324, 2756, 4052, 4484 (mod 6480) the following formula is used:

$54x+2=(29484x^2+2211x+43)^3+(-29484x^2-2157x-41)^3+(9828x^2+485x+4)^3+(-9828x^2-971x-22)^3$

If n = 254, 902, 1442, 1874, 1982, 2414, 3062, 3494, 3602, 4034, 4142, 5114, 5222, 5654, 5762, 6302 (mod 6480) a method due to Demjanenko is used. Notice that the results can have hundreds of digits in this case.

In the remaining cases the number n is replaced by −n and then all solutions are multiplied by −1.

王守恩 · 发表于前天 07:45

嗨！$(k1)^3+(k2)^3+(k3)^3+(k4)^3+(k5)^3=n$  可以有通项公式！——链接——如何求整数m表示为五个立方数之和的所有参数化形式？

问:  6m能表示为五个立方数之和的参数化形式:$6m=(36t^3+m+1)^3+(36t^3+m-1)^3+2(-36t^3-m)^3+(-6t)^3$，其中t为参数，对于不是6的倍数的整数m如何求参数化形式？

答: $6m+k^3=(m+1)^3+(m-1)^3+(-m)^3+(-m)^3+k^3$  ——故

$6m+0=6(m+0)+0=(m+1)^3+(m-1)^3+(-m)^3+(-m)^3+0^3$

$6m+1=6(m+0)+1=(m+1)^3+(m-1)^3+(-m)^3+(-m)^3+1^3$

$6m+2=6(m-1)+8=m^3+(m-2)^3+ (-m+1)^3+ (-m+1)^3+2^3$

$6m+3=6(m-4)+27=(m-3)^3+(m-5)^3+(-m+4)^3+(-m+4)^3+3^3$

$6m+4=6(m+2)-8=(m+3)^3+(m+1)^3+ (-m-2)^3+ (-m-2)^3+(-2)^3$

$6m+5=6(m+1)-1=(m+2)^3+m^3+(-m-1)^3+(-m-1)^3+(-1)^3$

故任意整数都可以表示为五个立方数之和。

王守恩 · 发表于前天 11:52

楼上的6个公式可以合并成1个公式。

$n=\bigg(\big\lfloor\frac{n}{6}\big\rfloor + 1 - x\bigg)^3 +\bigg (\big\lfloor\frac{n}{6}\big\rfloor - 1 - x\bigg)^3+ \bigg(-\big\lfloor\frac{n}{6}\big\rfloor + x\bigg)^3 + \bigg(-\big\lfloor\frac{n}{6}\big\rfloor + x\bigg)^3 + \bigg(Mod[n, 6] - 6\big\lfloor\frac{Mod[n, 6]}{4}\big\rfloor\bigg)^3$

$x=\big\lfloor\frac{Mod[n, 6]}{2}\big\rfloor + 3\big\lfloor\frac{Mod[n, 6]}{3}\big\rfloor - 7\big\lfloor\frac{Mod[n, 6]}{4}\big\rfloor +\big \lfloor\frac{Mod[n, 6]}{5}\big\rfloor$

王守恩 · 发表于昨天 04:48

楼上的公式搞复杂了。仔细看。

$00=1^3-1^3-0^3-0^3+0^3$
$01=1^3-1^3-0^3-0^3+1^3$
$02=0^3-2^3+1^3+1^3+2^3$
$03=3^3-5^3+4^3+4^3-3^3$
$04=3^3+1^3-2^3-2^3-2^3$
$05=2^3+0^3-1^3-1^3-1^3$
$06=2^3+0^3-1^3-1^3+0^3$
$07=2^3+0^3-1^3-1^3+1^3$
$08=1^3-1^3-0^3-0^3+2^3$
$09=3^3-4^3+3^3+3^3-2^3$
$10=4^3+2^3-3^3-3^3-2^3$
$11=3^3+1^3-2^3-2^3-1^3$
$12=3^3+1^3-2^3-2^3+0^3$
$13=3^3+1^3-2^3-2^3+1^3$
$14=2^3+0^3-1^3-1^3+2^3$
$15=3^3-3^3+2^3+2^3-1^3$
$16=5^3+3^3-4^3-4^3-2^3$
$17=4^3+2^3-3^3-3^3-1^3$
$18=4^3+2^3-3^3-3^3-0^3$
$19=4^3+2^3-3^3-3^3+1^3$
$20=3^3+1^3-2^3-2^3+2^3$
$21=0^3-2^3+1^3+1^3+3^3$
$22=6^3+4^3-5^3-5^3-2^3$
$23=5^3+3^3-4^3-4^3-1^3$
$24=5^3+3^3-4^3-4^3-0^3$
$25=5^3+3^3-4^3-4^3+1^3$
$26=4^3+2^3-3^3-3^3+2^3$
$27=1^3-1^3-0^3-0^3+3^3$
$28=7^3+5^3-6^3-6^3-2^3$
$29=6^3+4^3-5^3-5^3-1^3$
$30=6^3+4^3-5^3-5^3-0^3$
$31=6^3+4^3-5^3-5^3+1^3$
$32=5^3+3^3-4^3-4^3+2^3$
$33=2^3+0^3-1^3-1^3+3^3$
$34=8^3+6^3-7^3-7^3-2^3$
$35=7^3+5^3-6^3-6^3-1^3$
$36=7^3+5^3-6^3-6^3-0^3$
$37=7^3+5^3-6^3-6^3+1^3$
$38=6^3+4^3-5^3-5^3+2^3$
$39=3^3+1^3-2^3-2^3+3^3$
$40=9^3+7^3-8^3-8^3-2^3$
$41=8^3+6^3-7^3-7^3-1^3$
$42=8^3+6^3-7^3-7^3-0^3$
$43=8^3+6^3-7^3-7^3+1^3$
$44=7^3+5^3-6^3-6^3+2^3$
$45=4^3+2^3-3^3-3^3+3^3$

只要一串数就够了——{-1, -1, -2, -5, 1, 0, 0, 0, -1, -4, 2, 1, 1, 1, 0, -3, 3, 2, 2, 2, 1, -2, 4, 3, 3, 3, 2, -1, 5, 4, 4, 4, 3, 0, 6, 5, 5, 5, 4, 1, 7, 6, 6, 6, 5, 2, 8, 7, 7, 7, 6, 3, 9, 8, 8, 8, 7, 4, 10, 9, 9, 9, 8, 5, 11, 10, 10, 10, 9, 6, 12, 11, 11, 11, 10, 7, 13}

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {-1, -1, -2, -5, 1, 0, 0}, 90]

王守恩 · 发表于昨天 17:46

$00=1^3-1^3-0^3-0^3+0^3$
$01=1^3-1^3-0^3-0^3+1^3$
$02=0^3-2^3+1^3+1^3+2^3$
$03=3^3-5^3+4^3+4^3-3^3$
$04=3^3+1^3-2^3-2^3-2^3$
$05=2^3+0^3-1^3-1^3-1^3$
$06=2^3+0^3-1^3-1^3+0^3$
$07=2^3+0^3-1^3-1^3+1^3$
$08=1^3-1^3-0^3-0^3+2^3$
$09=3^3-4^3+3^3+3^3-2^3$
$10=4^3+2^3-3^3-3^3-2^3$
$11=3^3+1^3-2^3-2^3-1^3$
$12=3^3+1^3-2^3-2^3+0^3$
$13=3^3+1^3-2^3-2^3+1^3$
$14=2^3+0^3-1^3-1^3+2^3$
$15=3^3-3^3+2^3+2^3-1^3$
$16=5^3+3^3-4^3-4^3-2^3$
$17=4^3+2^3-3^3-3^3-1^3$
$18=4^3+2^3-3^3-3^3-0^3$
$19=4^3+2^3-3^3-3^3+1^3$
$20=3^3+1^3-2^3-2^3+2^3$
$21=0^3-2^3+1^3+1^3+3^3$
$22=6^3+4^3-5^3-5^3-2^3$
$23=5^3+3^3-4^3-4^3-1^3$
$24=5^3+3^3-4^3-4^3-0^3$
$25=5^3+3^3-4^3-4^3+1^3$
$26=4^3+2^3-3^3-3^3+2^3$
$27=1^3-1^3-0^3-0^3+3^3$
$28=7^3+5^3-6^3-6^3-2^3$
$29=6^3+4^3-5^3-5^3-1^3$
$30=6^3+4^3-5^3-5^3-0^3$

{0, 0, -1, -4, 2, 1, 1, 1, 0, -3, 3, 2, 2, 2, 1, -2, 4, 3, 3, 3, 2, -1, 5, 4, 4, 4, 3, 0, 6, 5, 5, 5, 4, 1, 7, 6, 6, 6, 5, 2, 8, 7, 7, 7, 6, 3, 9, 8, 8, 8, 7, 4, 10, 9, 9, 9, 8, 5, 11, 10, 10, 10, 9, 6, 12, 11, 11, 11, 10, 7, 13, 12, 12, 12, 11, 8, 14, 13, 13, 13, 12, 9}

Table[(n - (Mod[n, 6] - 6 Floor[Mod[n, 6]/4])^3)/6, {n, 0, 90}]——第3个数也可以这样出来。

也就是——Table[x = (n - (Mod[n, 6] - 6 Floor[Mod[n, 6]/4])^3)/6; (x + 1)^3 + (x - 1)^3 - 2 x^3 + (n - 6 x), {n, 0, 60}]

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66}

王守恩 · 发表于昨天 17:47

a,b,c,d = 正整数$a^3 + b^3 + c^3 - d^3 = n$。n能跑遍所有正整数,没问题。——约定1 ≤ a ≤ b ≤ c ≤ d ≤ 1000——这个a不是最小的。我就想看看最小的a,——就得动1000,动1000——电脑就罢工了。

Table[FindInstance[{a^3 + b^3 + c^3 - d^3 == n, 1 ≤ a ≤ b ≤ c ≤ d ≤ 1000}, {a, b, c, d}, Integers, 1], {n, 100}]
{{{a -> 4, b -> 4, c -> 6, d -> 7}}, {{a -> 1, b -> 1, c -> 1, d -> 1}}, {{a -> 15, b -> 385, c -> 499, d -> 566}}, {{a -> 1, b -> 4, c -> 4, d -> 5}}, {{a -> 5, b -> 524, c -> 530, d -> 664}},
{{a -> 2, b -> 5, c -> 6, d -> 7}}, {{a -> 2, b -> 6, c -> 8, d -> 9}}, {{a -> 1, b -> 32, c -> 104, d -> 105}}, {{a -> 1, b -> 2, c -> 3, d -> 3}}, {{a -> 3, b -> 103, c -> 111, d -> 135}},
{{a -> 1, b -> 130, c -> 141, d -> 171}}, {{a -> 1, b -> 297, c -> 619, d -> 641}}, {{a -> 1, b -> 7, c -> 10, d -> 11}}, {{a -> 5, b -> 296, c -> 881, d -> 892}}, {{a -> 2, b -> 32, c -> 104, d -> 105}},
{{a -> 2, b -> 2, c -> 3, d -> 3}}, {{a -> 3, b -> 3, c -> 3, d -> 4}}, {{a -> 1, b -> 25, c -> 50, d -> 52}}, {{a -> 1, b -> 75, c -> 215, d -> 218}}, {{a -> 1, b -> 26, c -> 76, d -> 77}},
{{a -> 1, b -> 21, c -> 55, d -> 56}}, {{a -> 1, b -> 28, c -> 85, d -> 86}}, {{a -> 2, b -> 23, c -> 44, d -> 46}}, {{a -> 5, b -> 167, c -> 621, d -> 625}}, {{a -> 1, b -> 8, c -> 8, d -> 10}},
{{a -> 2, b -> 75, c -> 215, d -> 218}}, {{a -> 1, b -> 87, c -> 468, d -> 469}}, {{a -> 1, b -> 3, c -> 3, d -> 3}}, {{a -> 1, b -> 13, c -> 14, d -> 17}}, {{a -> 1, b -> 13, c -> 18, d -> 20}},
{{a -> 58, b -> 511, c -> 667, d -> 755}}, {{a -> 2, b -> 8, c -> 8, d -> 10}}, {{a -> 5, b -> 5, c -> 8, d -> 9}}, {{a -> 2, b -> 87, c -> 468, d -> 469}}, {{a -> 2, b -> 3, c -> 3, d -> 3}},
{{a -> 2, b -> 13, c -> 14, d -> 17}}, {{a -> 1, b -> 40, c -> 71, d -> 75}}, {{a -> 1, b -> 37, c -> 50, d -> 56}}, {{a -> 1, b -> 16, c -> 25, d -> 27}}, {{a -> 7, b -> 241, c -> 532, d -> 548}},
{{a -> 17, b -> 17, c -> 23, d -> 28}}, {{a -> 2, b -> 5, c -> 5, d -> 6}}, {{a -> 4, b -> 11, c -> 14, d -> 16}}, {{a -> 1, b -> 8, c -> 12, d -> 13}}, {{a -> 2, b -> 37, c -> 50, d -> 56}},
{{a -> 1, b -> 256, c -> 533, d -> 552}}, {{a -> 1, b -> 19, c -> 26, d -> 29}}, {{a -> 1, b -> 6, c -> 7, d -> 8}}, {{a -> 4, b -> 262, c -> 265, d -> 332}}, {{a -> 23, b -> 29, c -> 77, d -> 79}},
{{a -> 2, b -> 8, c -> 12, d -> 13}}, {{a -> 1, b -> 602, c -> 659, d -> 796}}, {{a -> 2, b -> 256, c -> 533, d -> 552}}, {{a -> 3, b -> 3, c -> 3, d -> 3}}, {{a -> 1, b -> 192, c -> 353, d -> 371}},
{{a -> 1, b -> 62, c -> 103, d -> 110}}, {{a -> 1, b -> 31, c -> 42, d -> 47}}, {{a -> 1, b -> 25, c -> 34, d -> 38}}, {{a -> 2, b -> 602, c -> 659, d -> 796}}, {{a -> 5, b -> 348, c -> 770, d -> 793}},
{{a -> 2, b -> 80, c -> 237, d -> 240}}, {{a -> 1, b -> 668, c -> 845, d -> 966}}, {{a -> 1, b -> 22, c -> 41, d -> 43}}, {{a -> 1, b -> 102, c -> 146, d -> 161}}, {{a -> 1, b -> 4, c -> 8, d -> 8}},
{{a -> 1, b -> 85, c -> 91, d -> 111}}, {{a -> 4, b -> 4, c -> 4, d -> 5}}, {{a -> 5, b -> 95, c -> 185, d -> 193}}, {{a -> 2, b -> 668, c -> 845, d -> 966}}, {{a -> 1, b -> 95, c -> 377, d -> 379}},
{{a -> 1, b -> 11, c -> 20, d -> 21}}, {{a -> 2, b -> 4, c -> 4, d -> 4}}, {{a -> 1, b -> 7, c -> 9, d -> 10}}, {{a -> 1, b -> 29, c -> 43, d -> 47}}, {{a -> 4, b -> 297, c -> 619, d -> 641}},
{{a -> 4, b -> 7, c -> 10, d -> 11}}, {{a -> 2, b -> 95, c -> 377, d -> 379}}, {{a -> 2, b -> 11, c -> 20, d -> 21}}, {{a -> 1, b -> 26, c -> 53, d -> 55}}, {{a -> 2, b -> 7, c -> 9, d -> 10}},
{{a -> 1, b -> 260, c -> 282, d -> 342}}, {{a -> 1, b -> 12, c -> 12, d -> 15}}, {{a -> 3, b -> 31, c -> 42, d -> 47}}, {{a -> 1, b -> 22, c -> 24, d -> 29}}, {{a -> 4, b -> 28, c -> 85, d -> 86}},
{{a -> 2, b -> 26, c -> 53, d -> 55}}, {{a -> 8, b -> 14, c -> 32, d -> 33}}, {{a -> 2, b -> 260, c -> 282, d -> 342}}, {{a -> 2, b -> 12, c -> 12, d -> 15}}, {{a -> 1, b -> 6, c -> 6, d -> 7}},
{{a -> 1, b -> 13, c -> 26, d -> 27}}, {{a -> 1, b -> 192, c -> 364, d -> 381}}, {{a -> 4, b -> 13, c -> 18, d -> 20}}, {{a -> 31, b -> 94, c -> 535, d -> 536}}, {{a -> 20, b -> 38, c -> 38, d -> 49}},
{{a -> 3, b -> 95, c -> 377, d -> 379}}, {{a -> 1, b -> 14, c -> 20, d -> 22}}, {{a -> 1, b -> 17, c -> 18, d -> 22}}, {{a -> 1, b -> 9, c -> 14, d -> 15}}, {{a -> 1, b -> 16, c -> 36, d -> 37}}}
ParallelTable[a /. First@FindInstance[{a^3 + b^3 + c^3 - d^3 == n, 1 ≤ a ≤ b ≤ c ≤ d ≤ 1000}, {a, b, c, d}, Integers, 1], {n, 1000}]
4, 1, 15, 1, 5, 2, 2, 1, 1, 3, 1, 1, 1, 5, 2, 2, 3, 1, 1, 1, 1, 1, 2, 5, 1, 2, 1, 1, 1, 1, 58, 2, 5, 2, 2, 2, 1, 1, 1, 7, 17, 2, 4, 1, 2, 1, 1, 1, 4, 23, 2, 1, 2, 3, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 1, 4, 5, 2, 1, 1, 2, 1, 1, 4, 4, 2, 2,
1, 2, 1, 1, 3, 1, 4, 2, 8, 2, 2, 1, 1, 1, 4, 31, 20, 3, 1, 1, 1, 1, 4, 1, 1, 2, 2, 2, 1, 3, 2, 1, 4, 10, 11, 2, 4, 1, 2, 3, 1, 4, 1, 26, 2, 3, 3, 1, 1, 4, 3, 1, 26, 5, 2, 1, 1, 3, 1, 7, 7, 5, 2, 1, 5, 2, 1, 5, 1, 16, 2, 11, 1, 1, 1, 1,
1, 1, 13, 2, 2, 1, 1, 1, 2, 12, 4, 4, 2, 2, 1, 4, 1, 1, 3, 7, 1, 2, 3, 2, 2, 1, 3, 1, 1, 1, 17, 3, 2, 1, 2, 1, 1, 1, 1, 5, 2, 5, 2, 1, 1, 1, 1, 1, 5, 9, 8, 2, 1, 1, 1, 1, 70, 74, 14, 2, 2, 1, 1, 1, 1, 7, 5, 5, 1, 1, 1, 1, 1, 3, 10, 2, 2,
2, 1, 2, 1, 1, 6, 4, 23, 2, 8, 1, 1, 3, 1, 1, 1, 26, 2, 2, 3, 1, 1, 1, 4, 4, 8, 5, 2, 1, 1, 1, 4, 1, 4, 5, 2, 2, 2, 4, 1, 3, 1, 7, 5, 5, 5, 2, 1, 1, 1, 1, 10, 5, 5, 2, 1, 1, 1, 3, 9, 13, 5, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 4,
4, 2, 2, 3, 2, 2, 1, 1, 6, 13, 20, 3, 3, 1, 1, 1, 3, 3, 7, 8, 2, 1, 2, 1, 1, 1, 1, 1, 2, 21, 1, 2, 1, 1, 1, 1, 10, 2, 5, 2, 1, 1, 1, 7, 7, 7, 23, 2, 2, 1, 1, 3, 1, 1, 4, 8, 2, 2, 3, 1, 1, 1, 7, 1, 8, 6, 1, 1, 1, 4, 2, 7, 1, 2, 2, 2, 3, 4,
1, 2, 1, 13, 8, 8, 1, 2, 3, 1, 4, 1, 4, 2, 3, 3, 2, 1, 1, 1, 1, 10, 35, 5, 1, 1, 1, 1, 3, 6, 1, 2, 2, 2, 1, 3, 1, 1, 4, 28, 5, 2, 1, 1, 1, 1, 1, 9, 4, 2, 2, 2, 2, 1, 1, 1, 3, 4, 20, 5, 2, 1, 1, 1, 7, 4, 1, 5, 2, 1, 1, 1, 1, 2, 1, 7, 2, 2,
1, 1, 1, 1, 1, 4, 7, 2, 2, 2, 1, 1, 1, 6, 1, 4, 11, 2, 2, 1, 3, 1, 3, 1, 1, 8, 2, 3, 1, 1, 1, 1, 1, 16, 5, 2, 2, 2, 1, 1, 1, 10, 10, 11, 6, 1, 1, 1, 1, 1, 3, 4, 2, 2, 2, 1, 1, 3, 1, 1, 1, 8, 2, 1, 3, 2, 1, 1, 1, 7, 8, 3, 1, 2, 1, 1, 1, 4,
7, 2, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 10, 8, 3, 2, 1, 1, 1, 1, 1, 1, 17, 2, 1, 2, 1, 1, 2, 1, 16, 2, 5, 1, 2, 1, 2, 3, 1, 4, 2, 5, 2, 1, 3, 1, 1, 3, 31, 20, 2, 4, 1, 2, 1, 1, 7, 31, 8, 2, 4, 1, 1, 1, 3, 4, 4, 11, 2, 2, 1,
1, 3, 1, 1, 1, 14, 2, 2, 4, 1, 1, 1, 1, 4, 5, 5, 2, 1, 1, 1, 1, 4, 7, 17, 2, 2, 2, 2, 1, 1, 3, 13, 5, 11, 11, 1, 1, 1, 1, 1, 10, 5, 2, 2, 1, 1, 1, 1, 6, 1, 5, 2, 2, 1, 1, 1, 2, 7, 1, 8, 2, 2, 2, 1, 1, 1, 4, 1, 41, 5, 2, 1, 1, 1, 1, 3, 10,
5, 2, 1, 1, 1, 1, 1, 3, 10, 2, 2, 2, 2, 1, 1, 1, 1, 1, 11, 5, 2, 2, 2, 1, 1, 1, 1, 26, 3, 3, 1, 1, 1, 2, 7, 4, 8, 2, 2, 1, 1, 3, 1, 1, 4, 14, 2, 2, 8, 1, 2, 1, 1, 4, 14, 6, 2, 3, 1, 1, 1, 13, 1, 17, 5, 2, 1, 1, 3, 1, 6, 1, 11, 2, 1, 3, 1,
1, 1, 1, 4, 2, 5, 2, 2, 2, 1, 1, 3, 4, 11, 5, 3, 2, 1, 1, 1, 3, 7, 20, 3, 1, 1, 2, 1, 3, 4, 13, 2, 8, 5, 1, 1, 1, 1, 4, 16, 8, 2, 1, 2, 1, 3, 1, 1, 4, 2, 3, 1, 4, 1, 2, 4, 7, 4, 2, 8, 2, 3, 1, 1, 4, 4, 10, 8, 3, 2, 2, 1, 1, 3, 1, 28, 8, 3,
1, 1, 1, 1, 1, 1, 10, 2, 2, 2, 1, 1, 1, 1, 7, 7, 14, 2, 2, 1, 1, 4, 1, 1, 10, 53, 2, 2, 3, 1, 1, 1, 4, 13, 8, 5, 2, 1, 1, 3, 1, 1, 7, 5, 2, 2, 3, 1, 2, 3, 1, 22, 8, 11, 2, 1, 3, 1, 7, 1, 7, 23, 2, 3, 1, 1, 1, 1, 1, 19, 5, 2, 2, 1, 1, 1, 3,
1, 1, 14, 2, 2, 1, 3, 1, 1, 1, 25, 5, 2, 3, 1, 1, 2, 1, 12, 22, 5, 2, 2, 3, 1, 1, 3, 3, 25, 14, 8, 1, 2, 1, 1, 3, 1, 7, 2, 8, 2, 1, 6, 1, 1, 1, 28, 5, 2, 5, 1, 1, 1, 4, 4, 10, 35, 2, 1, 1, 1, 1, 1, 1, 4, 2, 2, 2, 1, 2, 1}

账号		自动登录	找回密码
密码			欢迎注册

[讨论] (k1)^3+(k2)^3+(k3)^3=n^3