On the exponential Diophantine equation (12m^2+1)^x+(13m^2-1)^y=(5m)^z

Abstract

Let m be a positive integer. Then we show that the exponential Diophantine equation (12m 2 + 1) x + (13m 2 1) y = (5m) z has only the positive integer solution (x;y;z) = (1;1;2) under some conditions. The proof is based on elementary methods and Baker’s method. Mathematics Subject Classication: 11D61