Fibonacci and Lucas numbers as products of three repdigits in base \(g\)
DOI10.1007/S12215-023-00878-4arXiv2212.14247MaRDI QIDQ6183471
Alan Filipin, Kouèssi Norbert Adédji, Alain S. Togbé
Publication date: 4 January 2024
Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2212.14247
Fibonacci numbersLucas numberslinear forms in logarithmsreduction methodMersenne numbersDiophantine equations\(g\) repdigit
Computer solution of Diophantine equations (11Y50) Diophantine equations in many variables (11D72) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)
Cites Work
- Fibonacci or Lucas numbers which are products of two repdigits in base \(b\)
- On the solutions of the Diophantine equation \(F_n \pm \frac{a (10^m - 1)}{9} = k!\)
- Tribonacci numbers that are concatenations of two repdigits
- Padovan and Perrin numbers which are products of two repdigits in base \(b\)
- Repdigits base \(b\) as products of two Pell numbers or Pell-Lucas numbers
- Linear combinations of factorials and \(S\)-units in a binary recurrence sequence
- Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
- An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
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