On the Diophantine equation a^x+b^y=z^2 where a\equiv 1 (mod 3) and b\equiv 1 (mod 3)

In this article, we show that the Diophantine equation a^x+b^y=z^2 has no non-negative integer solution, where a,b are positive odd integers with a\equiv 1 (mod 3), b\equiv 1 (mod 3), and x, y, z are non-negative integers.

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Publication Details

Journal
International journal of mathematics and computer science
Published
2025-01-01
DOI
https://doi.org/10.69793/ijmcs/02.2025/wanna
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00

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article

On the Diophantine equation a^x+b^y=z^2 where a\equiv 1 (mod 3) and b\equiv 1 (mod 3)

Somnuk Srisawat, Wanna Sriprad
International journal of mathematics and computer science
Algebraic Geometry and Number Theory
article

On the Diophantine equation a^x+b^y=z^2 where a\equiv 1 (mod 3) and b\equiv 1 (mod 3)

Somnuk Srisawat, Wanna Sriprad
article en

Abstract

In this article, we show that the Diophantine equation a^x+b^y=z^2 has no non-negative integer solution, where a,b are positive odd integers with a\equiv 1 (mod 3), b\equiv 1 (mod 3), and x, y, z are non-negative integers.

International journal of mathematics and computer science
Rajamangala University of Technology (TH)
Rajamangala University of Technology Thanyaburi
Openalex Percentile: Top 90%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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On the Diophantine equation a^x+b^y=z^2 where a\equiv 1 (mod 3) and b\equiv 1 (mod 3) — Somnuk Srisawat, Wanna Sriprad · International journal of mathematics and computer science (2025) | TGRS Research Map | TGRS