(Exponential Diophantine Equation n2􀀀1 )u +n2v = w2;n = 2;3;4;5

G Janaki; A Gowri Shankari

doi:10.17485/IJST/v17i2.2544

Article

(Exponential Diophantine Equation n2􀀀1 )u +n2v = w2;n = 2;3;4;5

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i2.2544

Year: 2024, Volume: 17, Issue: 2, Pages: 166-170

Original Article

(Exponential Diophantine Equation n2􀀀1 )u +n2v = w2;n = 2;3;4;5

G Janaki¹, A Gowri Shankari^2*

¹Associate Professor, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy - 18, Tamil Nadu, India
²Assistant Professor, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy - 18, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:08 October 2023, Accepted Date:08 December 2023, Published Date:12 January 2024

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

Abstract

Objectives: Diophantine research focuses on various ways to tackle multivariable and multidegree Diophantine problems. A Diophantine equation is a polynomial equation with only integer solutions. The objective of this manuscript is to find the solutions to a few exponential Diophantine equations and . Also generalize the Exponential equation , and of the form and explore that it has at least one solution as . Methods: Diophantine equations may have finite, infinite or no solutions in integers. There is no universal method for finding solutions to Diophantine equations. The particular type of Exponential Diophantine equation is analysed and generalised by the method of Catalan's conjecture. Findings: Exponential Diophantine equations and has only a finite number of solutions in (Whole numbers). The solution sets of , and are, respectively. Novelty: In this analysis, the particular type of Exponential Diophantine equation is analysed using elementary mathematics concepts instead of higher mathematics also generalize the Exponential equation , and of the form and explore that it has at least one solution as . 2020 Mathematical Subject Classification: 11D61.

Keywords: Catalan’s conjecture; Diophantine equation; Exponential Diophantine equation; Integral solutions; Non-negative integer solution

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Copyright

© 2024 Janaki & Shankari. 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)