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

2018/08/20 by LE Mao-hua, Reese Scott, Le, Maohua +3
Mathematics · Physics and Astronomy · #11D61 #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1808.06557

openalex publication_date 2018/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the conjecture of Jeśmanowicz
• An Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations II

Related

• A Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations
• An Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations II
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• At most one solution to a^x + b^y = c^z for some ranges of a, b, c
• On some conjectures of exponential Diophantine equations