不定方程y^3=x^2+260642的全部整数解

All Integeral Solutions of Diophantine Equation y^3= x^2+260642

借助于平方剩余的理论缩小解的范围,并且运用同余式、二次剩余及一些简单的初等方法,证明了不定方程y3=x2+260642仅有整数解(x,y)=(±1265,123)。

With the same square residual theory the scale of the solutions are reduced and by means of Congruence,quadratic residue and some of the simple elementary method,the diophantine equation y^3= x^2＋ 260642 is proved only integer solutions（ x,y） =（ ± 1265,123）.