如何求方程 x^3+2y^3=n 至少6种不同的(x,y)的整数解，其中gcd(x,y)=1？

northwolves

如何求方程 x^3+2y^3=k 至少n种不同的(x,y)的整数解k=a(n)，其中gcd(x,y)=1？

Solutions of Diophantine equation  x3+2y3=k


{1, 3, {1, 1}}
{2, 1, {{-1, 1}, {1, 0}}}
{3, 62, {{-34, 27}, {2, 3}, {4, -1}}}
{4, 899, {{-223, 177}, {-5, 8}, {11, -6}, {43, -34}}}
{5, 50466457, {{-269, 327}, {-71, 294}, {415, -219}, {739, -561}, {24697, -19602}}}

4  组解：{39302, 68923, 236629, 1092673, 2349397, 11678561, 26197387,  36097597，84697831, 87926959 ...}

5  组解：{818676613, 7040588227, 37127184317, 54827869519, 101346232114,  544456694611, ...}

northwolves

貌似$a(6)>10^{15}$

lsr314

你可以试一下只穷举那些素因子p满足x^3=2(mod p)有三个不同解的无平方因子n