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JP Journal of Algebra, Number Theory and Applications

JP Journal of Algebra, Number Theory and Applications
Volume 64, Issue 4, Pages 395 - 416 (July 2025)
http://dx.doi.org/10.17654/0972555525021

ON k-GENERALIZED PADOVAN NUMBERS WHICH ARE REPDIGITS IN BASE η

Hunar Sherzad Taher and Saroj Kumar Dash

Abstract:

Let k ≥ 3. Then the k-Padovan sequence is a generalization of the Padovan sequence. The sequence’s first k terms are 0, 0, ..., 0, 1, 1. This paper identifies all repdigits that can be expressed as k-Padovan numbers in base where through the application of the theory of linear forms in logarithms of algebraic numbers and a modified version of the Baker-Davenport reduction method.

Keywords and phrases:

Diophantine equations, linear forms in logarithms, k-Padovan numbers, repdigit, reduction method

Received: January 27, 2025; Accepted: May 9, 2025; Published: May 28, 2025

How to cite this article: Hunar Sherzad Taher and Saroj Kumar Dash, On k-generalized Padovan numbers which are repdigits in base h, JP Journal of Algebra, Number Theory and Applications 64(4) (2025), 395-416. https://doi.org/10.17654/0972555525021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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