求一组本原解

Klion

求方程a^3+b^3=c^2(c>=b>=a)的一组a>10000的本原解，本原解是不存在a1,b1,c1满足方程，而且a = a1*n^2,b = b1*n^2,c = c1*n^3(n>=2)
哪位高人说说，小弟感激不尽

wayne

给一个通式：
$a=4 m n (3 m^2 - 3 m n + n^2)$
$b=(m - n) (3 m - n) (3 m^2 + n^2)$
$c=(3 m^2 - n^2) (9 m^4 - 18 m^3 n + 18 m^2 n^2 - 6 m n^3 + n^4)$


还有一个：
$a = 3 s^4 + 6 s^2 t^2 - t^4$
$b =-3 s^4 + 6 s^2 t^2 + t^4$
$c=6 s t (3 s^4 + t^4)$

比如：
{10840, 78561, 22048559},
{13896, 43225, 9134819},
{21744, 29785, 6058403},
{15520, 12369, 2372903},
{66480, 99169, 35624303},
{38920,24081, 8539271},
{76944, 69745, 28192247},
{57376, 32025, 14890499},
{82896, 13825, 23922431}