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}