关于不定方程x^3+1=1043y^2的整数解

The Integral Solution of the Indeterminate Equation x^3+1=1043y^2

主要利用递归序列、同余、平方剩余以及Pell方程的解的性质,证明了不定方程x^3+1=1043y^2仅有平凡整数解(-1,0)。

In this paper, by using recursive sequences, congruence, quadratic residuals, and the property of the solution of the Pell equation ,it is proved that the indeterminate equatlonx^3 ＋ 1 = 1043y^2 has only trivial integer solution （ - 1,0）.