On the diophantine equation (la^x + mb^y = nc^z)

摘要

In this paper, we give an upper bound for the solutions x , y , z of the equation in the title, of magnitude $$left( log max {a, b, c}ight) ^{2 + epsilon }$$ log max { a , b , c } 2 + ? . This yields an improvement of earlier results of Hu and Le, where the bound is cubic in $$log max {a, b, c}$$ log max { a , b , c } .