On the exponential Diophantine equation mx + (m+1)y = (1+m plus m2)z

Abstract

Let m > 1 be a positive integer. We show that the exponential Diophantine equation m(x) + (m + 1)(y) = (1 + m + m(2))(z) has only the positive integer solution (x, y, z) = (2, 1, 1) when m >= 2.