A Paradigm for Two Classes of Simultaneous Exponential Diophantine Equations

V Pandichelvi; R Vanaja

doi:10.17485/IJST/v16i40.1643

Article

A Paradigm for Two Classes of Simultaneous Exponential Diophantine Equations

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i40.1643

Year: 2023, Volume: 16, Issue: 40, Pages: 3514-3521

Original Article

A Paradigm for Two Classes of Simultaneous Exponential Diophantine Equations

V Pandichelvi¹, R Vanaja^2*

¹Assistant Professor, PG & Research Department of Mathematics, Urumu Dhanalakshmi College,(Affiliated to Bharathidasan University), Trichy, India
²Assistant Professor, PG & Research Department of Mathematics, Shrimati Indira Gandhi College, (Affiliated to Bharathidasan University), Trichy, India

*Corresponding Author
Email: [email protected]

Received Date:04 July 2023, Accepted Date:28 September 2023, Published Date:27 October 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The goal of this article is to find integer solutions to two distinct kinds of simultaneous exponential Diophantine equations in three variables. Methods: The system of exponential Diophantine equations is translated into the eminent form of Thue equations, and then their generalised solutions satisfying certain conditions are applied. Findings: The finite set of integer solutions for two disparate categories of simultaneous exponential Diophantine equations consisting of three unknowns is scrutinized. In some circumstances, there is no solution in this analysis for both the dissimilar simultaneous Diophantine equations. Novelty: The motivation is considered to be two types of simultaneous exponential Diophantine equations are first converted into specific system of Pell equations, then into Thue equations for the possibilities of the sum of the exponents, such as or . If then, the equations are transformed into a cubic equation, which is not in the form of Pell equations. So, such cases are discarded for exploring solutions to the necessary equations.

Keywords: Simultaneous Exponential Equations, Simultaneous Pell Equations, Thue Equations, Integer Solutions, Divisibility

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Copyright

© 2023 Pandichelvi & Vanaja. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)