A Note on the Exponential Diophantine Equation (a^m-1)(b^n-1) = x^2

摘要

Let a and b be fixed positive integers.In this paper,using some elementary methods,we study the diophantine equation(a^m-1)(b^n-1)= x^2.For example,we prove that if a ≡ 2(mod 6),b ≡ 3(mod 12),then(a^n-1)(b^m-1)= x^2 has no solutions in positive integers n,m and x.