三个或四个整数的立方和是一个平方数问题

northwolves

1.若a(n) 为$x^3+y^3+z^3 =k^2，0<x<y<z$， 恰好有n组解的最小k值，是否对任意n值都可找到某个k?

2.若a(n) 为$x^3+y^3+z^3+w^3 =k^2，0<x<y<z<w$， 恰好有n组解的最小k值，是否对任意n值都可找到某个k?

northwolves

对于问题2，我曾经计算到$k<=500000$, 仅$n=1177和 n=1197$ 暂未找到解

northwolves

比如20个解的情况：{1134,{{8,73,75,78},{28,68,77,79},{29,67,73,83},{33,57,79,83},{35,58,70,89},{39,51,73,89},{18,27,81,90},{42,54,63,93},{5,46,71,94},{9,32,75,94},{9,58,59,96},{22,57,59,96},{3,57,60,96},{2,3,72,97},{26,33,64,99},{12,34,65,99},{16,44,55,101},{26,37,50,103},{22,39,45,104},{9,18,27,108}},20}

northwolves

我这里提交了两个序列，请大家批评指教：

a(n) is the smallest positive integer k such that the Diophantine equation x^3 + y^3 + z^3 = k^2, where 0 < x < y < z has exactly n integer solutions.

a(n) is the smallest positive integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^2, where 0 < x < y < z < w has exactly n integer solutions.