Fibonacci numbers which are concatenations of two repdigits

DOI10.2989/16073606.2019.1686439zbMath1472.11067OpenAlexW2987108330WikidataQ126833087 ScholiaQ126833087MaRDI QIDQ4986570

Alaa Altassan, Florian Luca, Hatoon Shoaib, Adel N. Alahmadi

Publication date: 27 April 2021

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2019.1686439

zbMATH Keywords

Fibonacci numbersrepdigitlinear forms in complex logarithms

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (17)

On the solutions of the Diophantine equation \(F_n \pm \frac{a (10^m - 1)}{9} = k!\) ⋮ \(k\)-generalized Pell numbers which are concatenation of two repdigits ⋮ On concatenations of two Padovan and Perrin numbers ⋮ On b -repdigits as product of consecutive of Lucas members ⋮ Balancing and Lucas-balancing numbers which are concatenation of three repdigits ⋮ Tribonacci numbers that are concatenations of two repdigits ⋮ Unnamed Item ⋮ Balancing numbers which are concatenation of two repdigits ⋮ Unnamed Item ⋮ Unnamed Item ⋮ k-generalized Fibonacci numbers which are concatenations of two repdigits ⋮ Padovan numbers which are palindromic concatenations of two distinct repdigits ⋮ Generalized Lucas numbers which are concatenations of two repdigits ⋮ Associated Pell numbers which are repdigits or concatenation of two repdigits ⋮ Tribonacci numbers with two blocks of repdigits ⋮ Padovan numbers that are concatenations of two distinct repdigits ⋮ On concatenations of Fibonacci and Lucas numbers

Cites Work

• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Distinct digits in basebexpansions of linear recurrence sequences
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• On a conjecture about repdigits in k-generalized Fibonacci sequences
• On terms of linear recurrence sequences with only one distinct block of digits
• On the representation of an integer in two different bases.
• On integers with identical digits
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