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.

 
  • 設p是大于3的奇素數,證明:方程2)()(zyxyxpp=--,1+>yx,1),gcd(=yx僅當p=5時(shí)有正整數解)11,1,3(),,(=zyx可使x是奇素數的方冪。
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