A Survey on the Ternary Purely Exponential Diophantine Equation $a^x + b^y = c^z$

Abstract

Let a, b, c be fixed coprime positive integers with min{a, b, c} > 1. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions (x, y, z) of the ternary purely exponential diophantine equation a x + b y = c z .