Rad HAZU, Matematičke znanosti, Vol. 30 (2026), 35-49. \( \)

ON \(b\)-REPDIGITS AS PRODUCTS OR SUMS OF FIBONACCI, PELL, BALANCING AND JACOBSTHAL NUMBERS

Chèfiath Awero Adégbindin, Kouèssi Norbert Adédji and Alain Togbé

Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Bénin
e-mail:adegbindinchefiath@gmail.com

Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Bénin
e-mail:adedjnorb1988@gmail.com

Department of Mathematics and Statistics, Purdue University Northwest, 2200 169th Street, Hammond, IN 46323 USA
e-mail:atogbe@pnw.edu

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.

2020 Mathematics Subject Classification.   11D09, 11B37, 11J68, 11Y50

Key words and phrases.   Fibonacci, Pell, balancing and Jacobsthal numbers, \(b\)-repdigits, logarithmic height, reduction method

Full text (PDF) (free access)

https://doi.org/10.21857/mnlqgcpvky

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