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.
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.
基金
Supported by the National Natural Science Foundation of China (Grant No.10901002)
