A Survey on the ternary purely exponential diophantine equation ax + by = cz

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 ax + by = cz.

Keywords

• ternary purely exponential diophantine equation
• Jesmanowicz conjecture
• Terai-Jesmanowicz conjecture