关于指数Diophantine方程(a^n-1)(b^n-1)=x^2

On the exponential Diophantine equation(a^n-1)(b^n-1)=x^2

设a,b是不同的正整数.运用初等数论方法证明了:当a≡0(mod 2)且b≡3(mod 8)时,方程(an-1)(bn-1)=x2没有适合n>1的正整数解(x,n).

Let a and b be distinct positive integers.It is proven using some elementary number theory methods that if a≡0(mod 2) and b≡3(mod 8),there is no positive integer solution of the exponential Diophantine equation when n>1.