关于不定方程x^3+1=2py^2

On the Diophantine Equation x^3+1=2py^2

利用递归数列和同余式证明不定方程x3+1=2py2在p≡5(mod8)的条件下,仅有整数解(x,y)=(-1,0)。

In this paper we have proved that the only solution in integers of the equation in the title is(x,y)=(-1,0) if and only if p=5(mod8).