关于三个连续正整数平方和中的素数方幂

On the prime powers in sums of squares of three consecutive positive integers

设x,n是正整数,p是素数。证明了:如果x^2+(x+1)~2+(x+2)~三= p^n,则必有n=1。

Let x, n be positive integers, and let p be a prime. In this paper we prove that if x2 + (x + 1)2+ (x + 2)2 = pn,then n=1.