关于Diophantine方程x^3-1=py^2

On the Diophantine equation x^3-1=py^2

设p是奇素数,证明了当p=12s2+1,其中s是奇数时,则方程x3-1=py2无正整数解(x,y)。

Let p be an odd prime. The result that if p=12s^2+1, where s is an odd integer, then the equation x^3-1=py^2 has no positive integer solutions (x,y)is proved.