On a variant of an identity relating cubes of three consecutive Fibonacci numbers

DOI10.1007/s40840-022-01439-1OpenAlexW4311705793MaRDI QIDQ2105923

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

Publication date: 8 December 2022

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-022-01439-1

zbMATH Keywords

Fibonacci numbersreduction methodlinear form in logarithmsDiophantine exponential equation

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
• On the Diophantine equation \(F_n^x+F_{n+1}^x=F_m^y\)
• Solving exponential diophantine equations using lattice basis reduction algorithms
• An exponential Diophantine equation related to powers of three consecutive Fibonacci numbers
• 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
• Problems in Algebraic Number Theory
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• Number Theory

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