Two \(b\)-repunits in the Fibonacci sequence

DOI10.1016/j.jnt.2020.10.006zbMath1468.11054OpenAlexW3113904968MaRDI QIDQ1998907

Jhonny C. Gómez, Florian Luca, Carlos Alexis Gómez Ruiz

Publication date: 9 March 2021

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2020.10.006

zbMATH Keywords

continued fractionsFibonacci numbersreduction methodsrepunitslower bounds for linear forms in logarithms

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Cites Work

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• Fibonacci numbers at most one away from a perfect power
• Linear forms in two logarithms and interpolation determinants
• Linear combinations of factorials and \(S\)-units in a binary recurrence sequence
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Some problems involving powers of integers
• A search for Fibonacci-Wieferich and Wolstenholme primes
• Problems in Algebraic Number Theory
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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