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

Scientific paper - Original scientific paper

• Author: Kouessi Norbert Adedji
• Author: Alan Filipin
• Author: Alain Togbe
• Author's institution: University of Zagreb; Faculty of Civil Engineering
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Civil Engineering

Abstract (english)

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 is done using linear forms in logarithms of algebraic numbers.

• Keywords (english): Fibonacci numbers; Lucas numbers; Mersenne numbers; Diophantine equations; g repdigit; Linear forms in logarithms; Reduction method
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Accepted
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Rendiconti del Circolo Matematico di Palermo
• Numbering: vol. n/a
• e-ISSN: 0009-725X
• URN:NBN: urn:nbn:hr:237:448477
• Publication: 2023
• Type of resource: Text
• Access conditions: Open access
• Created on: 2024-09-05 06:10:33