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

Autori
Adedji, Kouessi Norbert ; Filipin, Alan ; Togbe, Alain

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Rendiconti del Circolo Matematico di Palermo (2024)

Status rada
Prihvaćen

Ključne riječi
Fibonacci numbers ; Lucas numbers ; Mersenne numbers ; Diophantine equations ; g repdigit ; Linear forms in logarithms ; Reduction method

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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