On numbers n dividing the nth term of a linear recurrence

DOI10.1017/S0013091510001355zbMath1262.11015arXiv1010.4544MaRDI QIDQ2891984

Florian Luca, Juan José Alba González, Igor E. Shparlinski, Carl B. Pomerance

Publication date: 18 June 2012

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4544

zbMATH Keywords

linear recurrencedivisibilityLucas sequence

Mathematics Subject Classification ID

Recurrences (11B37) Congruences; primitive roots; residue systems (11A07) Distribution of integers with specified multiplicative constraints (11N25)

Related Items (17)

Index divisibility in the orbit of 0 for integral polynomials ⋮ The moments of the logarithm of a G.C.D. related to Lucas sequences ⋮ Distribution of integral values for the ratio of two linear recurrences ⋮ On Novák numbers ⋮ Greatest common divisors of shifted primes and Fibonacci numbers ⋮ On the greatest common divisor of n and the nth Fibonacci number, II ⋮ On numbers \(n\) relatively prime to the \(n\)th term of a linear recurrence ⋮ On numbers n dividing the nth term of a Lucas sequence ⋮ On the gcd's of \(k\) consecutive terms of Lucas sequences ⋮ Central binomial coefficients divisible by or coprime to their indices ⋮ ON NUMBERS WITH POLYNOMIAL IMAGE COPRIME WITH THE TH TERM OF A LINEAR RECURRENCE ⋮ The density of numbers \(n\) having a prescribed G.C.D. with the \(n\)th Fibonacci number ⋮ On the greatest common divisor of \(n\) and the \(n\)th Fibonacci number ⋮ The Distribution of Self-Fibonacci Divisors ⋮ An upper bound for the moments of a GCD related to Lucas sequences ⋮ The density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their indices ⋮ On terms in a dynamical divisibility sequence having a fixed g.c.d with their indices

Cites Work

• Unnamed Item
• Some divisibilities amongst the terms of linear recurrences
• On a problem of Oppenheim concerning Factorisatio Numerorum
• Multiplicities of recurrence sequences
• Existence of primitive divisors of Lucas and Lehmer numbers
• The Divisibility of an – bn by Powers of n
• Polynomial values free of large prime factors

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