On the solutions of the Diophantine equation \(F_n \pm \frac{a (10^m - 1)}{9} = k!\)

DOI10.1016/j.jnt.2021.12.008zbMath1498.11106OpenAlexW4225882269WikidataQ113870319 ScholiaQ113870319MaRDI QIDQ2161349

Florian Luca, Kouèssi Norbert Adédji, Alain S. Togbé

Publication date: 4 August 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.12.008

zbMATH Keywords

Fibonacci numbersreduction method\(p\)-adic valuation\(p\)-adic linear forms in logarithms of algebraic numbers

Mathematics Subject Classification ID

Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86) Diophantine equations (11D99)

Related Items (3)

On the solutions of the Diophantine equation \(P_n \pm \frac{a(10^m -1)}{9}=k!\) ⋮ Balancing numbers which are products of three repdigits in base \(b\) ⋮ Fibonacci and Lucas numbers as products of three repdigits in base \(g\)

Uses Software

• Maple

Cites Work

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• Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
• Sums of factorials in binary recurrence sequences
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• On a Diophantine equation involving Fibonacci numbers and the Ramanujan \(\tau\)-function of factorials
• Tribonacci numbers that are concatenations of two repdigits
• Factoriangular numbers in balancing and Lucas-balancing sequence
• Repdigits base \(b\) as products of two Pell numbers or Pell-Lucas numbers
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• A Remark on Stirling's Formula
• Lucas factoriangular numbers
• Pell factoriangular numbers
• Fibonacci numbers which are concatenations of two repdigits

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