Fibonacci and Lucas numbers as products of three repdigits in base g

2022/12/29 by Kouèssi Norbert Adédji, Adedji, Kouessi Norbert, Alan Filipin +3 · 2 citations
Mathematics · Physics and Astronomy · #11B39 #11D61 #11D72 #11J86 #11Y50 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.14247

openalex publication_date 2022/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recall that repdigit in base g is a positive integer that has only one digit in its base g expansion, i.e. a number of the form a(g^m-1)/(g-1), for some positive integers m≥ 1, g≥ 2 and 1≤ a≤ g-1. In the present study we investigate all Fibonacci or Lucas numbers which are expressed as products of three repdigits in base g. As illustration, we consider the case g=10 where we show that the numbers 144 and 18 are the largest Fibonacci and Lucas numbers which can be expressible as products of three repdigits respectively. All this can be done using linear forms in logarithms of algebraic numbers.

Cited by

• On Narayana numbers which are products of four b-repdigits with a consequence
• Thabit and Williams Numbers Base b as a Sum or Difference of Two g-Repdigits

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