Fermat $k$-Fibonacci and $k$-Lucas numbers

DOI10.21136/MB.2018.0015-18zbMath1474.11042MaRDI QIDQ3297059

Jose L. Herrera, Jhon J. Bravo

Publication date: 2 July 2020

Published in: Mathematica Bohemica (Search for Journal in Brave)

zbMATH Keywords

reduction methodFermat numberlinear form in logarithmsgeneralized Fibonacci number

Mathematics Subject Classification ID

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

Related Items (6)

On Fermat and Mersenne numbers expressible as product of two \(k\)-Fibonacci numbers ⋮ Coincidence between \(k\)-Fibonacci numbers and products of two Fermat numbers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Generalized Lucas numbers which are concatenations of two repdigits ⋮ Unnamed Item

Uses Software

• Mathematica

Cites Work

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• Repdigits in \(k\)-Lucas 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
• Applications of Number Theory to Numerical Analysis
• Coincidences in generalized Lucas sequences
• Powers of two as sums of two k-Fibonacci numbers
• A simplified Binet formula for k-generalized Fibonacci numbers
• On Fibonacci numbers which are one more than a square.

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