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。文章证明了:当p>3时,如果D不能被p或2kp+1形之素数整除,则方程xp+2p=Dy2没有适合gcd(x,y)=1的正整数解。

Let p be an odd prime and D be a positive integer with square free.It is proved in this paper that if p>3and D is not divisible by p or primes of the form2kp+1,the equation x p +2 p =Dy 2 has no positive integer solutions(x,y)with gcd(x,y)=1.