关于丢番图方程x^3+1=86y^2整数解的讨论

On the Integral Solutions of Diophantine Equation x^3+1=86y^2

利用递归数列、同余式证明了丢番图方程x3+1=86y2仅有整数解(x,y)=(-1,0),(7,±2)。

By using congruence and recurrent sequence,the author has proved that the Diophantine equation x^3 ＋ 1 =86y^2 has only the integer solution（x,y） = （ - 1,0）, （7, ±2）.