In this paper, let p be an odd prime with p>3, we prove that the equation (xp-yp)/(x-y)=z2 has only the positive integer solution (x, y, z, p)=(3,1,11,5), satisfying x>y+1. gcd (x, y)=1. As a result, x is an odd prime power.

• 设p是大于3的奇素数,证明:方程2)()(zyxyxpp=--,1+>yx,1),gcd(=yx仅当p=5时有正整数解)11,1,3(),,(=zyx可使x是奇素数的方幂。