On the Diophantine equation a^x+b^y=z^2

In this paper, we establish a non-existence condition for solutions of the Diophantine equation a^x+b^y=z^2. Moreover, we provide a short proof of some Diophantine theorems of Pakapongpun and Chattae \cite{PC} using our result

Authors

Pinya Ardsalee (ORCID: https://orcid.org/0000-0002-9211-8211)
Chaowat Manyuen (ORCID: https://orcid.org/0000-0002-9929-4090)

Publication Details

Journal: International journal of mathematics and computer science
Published: 2025-01-01
DOI: https://doi.org/10.69793/ijmcs/03.2025/chaowat
Primary Topic: Algebraic Geometry and Number Theory
Type: article
Field-Weighted Citation Impact: 0.00

Funders

Mahasarakham University

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article

On the Diophantine equation a^x+b^y=z^2

Pinya Ardsalee, Chaowat Manyuen

Jan 1, 2025

International journal of mathematics and computer science

Algebraic Geometry and Number Theory

article

On the Diophantine equation a^x+b^y=z^2

Pinya Ardsalee, Chaowat Manyuen

January 1, 2025article en

Abstract

International journal of mathematics and computer science

Mahasarakham University

Openalex Percentile: Top 83%

Algebraic Geometry and Number Theory

DOI Open Access PDF OpenAlex

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On the Diophantine equation a^x+b^y=z^2 — Pinya Ardsalee, Chaowat Manyuen · International journal of mathematics and computer science (2025) | TGRS Research Map | TGRS