Multiplicative independence in \(k\)-generalized Fibonacci sequences

DOI10.1007/s10986-016-9332-1zbMath1355.11010OpenAlexW2549640932MaRDI QIDQ507031

Florian Luca, Carlos Alexis Gómez Ruiz

Publication date: 3 February 2017

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-016-9332-1

zbMATH Keywords

lower bounds for nonzero linear forms in logarithms of algebraic numbersmultiplicatively independent integers\(k\)-generalized Fibonacci numbers

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)

Related Items (7)

Multiplicative Diophantine equations with factors from different Lucas sequences ⋮ \(k\)-Fibonacci powers as sums of powers of some fixed primes ⋮ Multiplicative dependent pairs in the sequence of Padovan numbers ⋮ On prime powers in linear recurrence sequences ⋮ The complete solution of the Diophantine equation \(\left(F_{n+1}^{(k)}\right)^x - \left(F_{n-1}^{(k)}\right)^x = F_m^{(k)}\) ⋮ Multiplicative dependence between Padovan and Perrin numbers ⋮ Multiplicative dependence between \(k\)-Fibonacci and \(k\)-Lucas numbers

Cites Work

• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• ON THE LARGEST PRIME FACTOR OF THE k-FIBONACCI NUMBERS
• On a conjecture about repdigits in k-generalized Fibonacci sequences
• Generalized Fibonacci Numbers and Associated Matrices
• A simplified Binet formula for k-generalized Fibonacci numbers
• On Generalized Fibonacci Numbers
• Number Theory
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