Products of $k$-Fibonacci numbers which are rep-digits

2020/97/1-2 (7) — DOI: 10.5486/PMD.2020.8725 — pp. 101-115

Authors: Adel Alahmadi, Alaa Altassan, Florian Luca and Hatoon Shoaib

Abstract:

We show that there are no examples of non-trivial products of consecutive $k$-Fibonacci numbers that are rep-digits.

Keywords: k-Fibonacci numbers, repdigits, linear forms in complex logarithms

Mathematics Subject Classification: 11B39, 11A25, 11J86