关于Diophantine方程x^p-2~p=Dy^2

On the Diophantine equation x^p-2~p=Dy^2

设p是奇素数,D是无平方因子正整数.本文证明了:当p>3时,如果D不能被p或2kp+1之形素数整除,则方程xp-2p=Dy2没有适合gcd(x,y)=1的正整数解(x,y).

Let p be an odd prime, and let D be a positive integer with square free. This paper prove that if p>3 and D is not divisible by p or primes of the form 2kp+1, then the equation x^(p)-2^(p)=Dy^(2) has no positive integer solutions ( x, y ) with gcd (x, y)=1.