On The diophantine equationFn+Fm=2a

DOI10.2989/16073606.2015.1070377zbMath1419.11024OpenAlexW2338783736MaRDI QIDQ5233929

Florian Luca, Jhon J. Bravo

Publication date: 9 September 2019

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

Full work available at URL: https://doi.org/10.2989/16073606.2015.1070377

zbMATH Keywords

Fibonacci numberslinear forms in logarithmsreduction methodZeckendorf representation

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)

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Cites Work

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• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• PV-numbers and sets of multiplicity
• Existence of primitive divisors of Lucas and Lehmer numbers
• 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 the representation of an integer in two different bases.
• On factorials expressible as sums of at most three Fibonacci numbers
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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