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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 570=30, 2026.

Original scientific paper

https://doi.org/10.21857/mnlqgcpvky

On b-repdigits as products or sums of Fibonacci, Pell, balancing and Jacobsthal numbers

Chèfiath Awero Adégbindin ; Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Bénin
Kouèssi Norbert Adédji orcid id orcid.org/0000-0001-8257-5729 ; Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Bénin
Alain Togbé orcid id orcid.org/0000-0002-5882-936X ; Department of Mathematics and Statistics, Purdue University Northwest, 2200 169th Street, Hammond, IN 46323 USA

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Abstract

Let \(b\ge 2\) be an integer. In this paper, we study the repdigits in base \(b\) that can be expressed as sums or products of Fibonacci, Pell, balancing and Jacobsthal numbers. The proofs of our main theorems use lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method.

Keywords

Fibonacci, Pell, balancing and Jacobsthal numbers; b-repdigits; logarithmic height; reduction method

Hrčak ID:

344360

URI

https://hrcak.srce.hr/344360

Publication date:

10.2.2026.

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