Original scientific paper
https://doi.org/10.21857/yl4okf8no9
A generalization of a theorem of Murat Alan
Mariama Ndao Faye
; UFR of Applied Sciences and Technology, University Gaston Berger, Sénégal
Kouèssi Norbert Adédji
; Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Bénin
Alain Togbé
; Department of Mathematics and Statistics, Purdue University Northwest, 2200 169th Street, Hammond, IN 46323 USA
Abstract
Let (Fn)n≥0 and (Ln)n≥0 be the Fibonacci and Lucas sequences respectively. In 2022, Murat Alan found all Fibonacci and Lucas numbers which are concatenations of two terms of the other sequence. Let b ≥ 2 be an integer. In this paper, we generalize the results of Murat Alan by considering the following Diophantine equations Fn = bdLm + Lk and Ln = bdFm + Fk in non-negative integers (n, m, k), where d denotes the number of digits of Lk and Fk in base b, respectively.
Keywords
Fibonacci numbers; Lucas numbers; b-concatenation; logarithmic height; reduction method
Hrčak ID:
326514
URI
Publication date:
9.1.2025.
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