The Integer Solutions to a Polynomial-Exponential Diophantine Equation in Three Variables

Abstract

The aim of the present article is to give a complete list of the integer solutions to polynomial-exponential Diophantine equations, as well as those to exponential Diophantine equations in three variables. Since there is no universal effective method to determine the integer solutions to these equations, our results give new examples in the cases where the theory of linear forms in logarithms cannot be applied.