关于Diophantine方程〔x 2〕-1=(q^n-1)/(q-1)

On the Diophantine Equation 〔x 2〕-1=(q^n-1)/(q-1)

设q=pr,其中p是素数,r是正整数.本文证明了:当p<100时,如果p≠2,13,17,19,43,47,53,59,67,83或89,则方程x-1=(qn-1)/(q-1)没有正整数解(x,n).

Let q = p＇, where p is a prime and r is a prime positive integer, In this paper we prove that if p 〈 100 and p≠2,13,17,19,43,47,53,59,67,83 or 89, then the equation（x2）-1=（q^n-1）/（q-1） has no positive integer solution （ x, n）.