What question did this study set out to answer?

This paper aims to explore how repdigits in base b can be represented using Fibonacci, Pell, balancing, and Jacobsthal numbers.

February 13, 2026Open Access

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

CAChèfiath AdegbindinInstitute of Mathematics and Physics KAKouèssi Norbert Adédji ATAlain Togbé

Key Points

This paper aims to explore how repdigits in base b can be represented using Fibonacci, Pell, balancing, and Jacobsthal numbers.
Analyzed the properties of repdigits in base b.
Applied lower bounds for linear forms in logarithms of algebraic numbers.
Utilized the Baker-Davenport reduction method for proofs.
Identified specific conditions under which b-repdigits are expressible as sums of the discussed number sequences.
Established relationships between b-repdigits and the different sequences, including Fibonacci and Pell.
Provided proofs that demonstrate the utilization of advanced mathematical techniques for these representations.

Abstract

Let \ (b 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.

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