It is proved 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=pDy~2 has no positive integer solutions (x,y) with gcd (x,y)=1.

• 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=pDy2没有适合gcd(x；y)=1的正整数解(x；y).