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Research Article | Open Access

Repdigits base $η$ as sum or product of Perrin and Padovan numbers

Hunar Sherzad Taher, Saroj Kumar Dash(

)

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600127, India

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Abstract

Let ${E_{n}}_{n \geq 0}$ and ${P_{n}}_{n \geq 0}$ be sequences of Perrin and Padovan numbers, respectively. We have found all repdigits that can be written as the sum or product of $E_{n}$ and $P_{m}$ in the base $η$ , where $2 \leq η \leq 10$ and $m \leq n$ . In addition, we have applied the theory of linear forms in logarithms of algebraic numbers and Baker-Davenport reduction method in Diophantine approximation approaches.

Keywords

exponential Diophantine equation repdigit linear forms in logarithms Padovan numbers Perrin numbers

CLC number: 11B39, 11D45, 11D61, 11J70, 11J86

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AIMS Mathematics

Volume 9 Issue 8,
August 2024

Pages 20173-20192

DOI: 10.3934/math.2024983

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Cite this article:

Taher HS, Dash SK. Repdigits base

η

as sum or product of Perrin and Padovan numbers. AIMS Mathematics, 2024, 9(8): 20173-20192. https://doi.org/10.3934/math.2024983

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Received: 08 February 2024

Revised: 08 May 2024

Accepted: 10 May 2024

Published: 15 August 2024

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)