Common values of generalized Fibonacci and Pell sequences

DOI10.1016/j.jnt.2021.03.001zbMath1471.11049OpenAlexW3138279123MaRDI QIDQ2031264

Jose L. Herrera, Jhon J. Bravo, Florian Luca

Publication date: 8 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.03.001

zbMATH Keywords

reduction methodlinear form in logarithms\(\ell\)-Fibonacci number\(k\)-Pell number

Mathematics Subject Classification ID

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

Related Items (10)

$k$-generalized Pell numbers which are repdigits in base $b$ ⋮ On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers ⋮ \(k\)-generalized Pell numbers which are concatenation of two repdigits ⋮ On the multiplicative independence of the roots of generalized Fibonacci and Pell polynomials ⋮ On perfect powers in $k$-generalized Pell sequence ⋮ On perfect powers in \(k\)-generalized Pell-Lucas sequence ⋮ On repdigits which are sums or differences of two \(k\)-Pell numbers ⋮ Matrix structure of Jacobsthal numbers ⋮ Generalization of a theorem of Adegbindin, Luca and Togbé ⋮ Unnamed Item

Cites Work

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• The proof of a conjecture concerning the intersection of \(k\)-generalized Fibonacci sequences
• Intersection des images de certaines suites recurrentes linéaires
• Coincidences in generalized Fibonacci sequences
• Fibonacci numbers in generalized Pell sequences
• The generalized Binet formula, representation and sums of the generalized order-\(k\) Pell numbers
• The Binet formula, sums and representations of generalized Fibonacci \(p\)-numbers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Clases de potencias de dos en sucesiones k-generalizadas de Fibonacci
• On a conjecture about repdigits in k-generalized Fibonacci sequences
• Mersenne k-Fibonacci numbers
• On the Intersections of Fibonacci, Pell, and Lucas Numbers
• A Diophantine equation in $k$-Fibonacci numbers and repdigits
• On a generalization of the Pell sequence
• Products of $k$-Fibonacci numbers which are rep-digits
• Powers of two as sums of two k-Fibonacci numbers
• A simplified Binet formula for k-generalized Fibonacci numbers

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