ON NUMBERS WITH POLYNOMIAL IMAGE COPRIME WITH THE TH TERM OF A LINEAR RECURRENCE

DOI10.1017/S0004972718000606zbMath1475.11027arXiv1805.05114MaRDI QIDQ4645762

Daniele Mastrostefano, Carlo Sanna

Publication date: 10 January 2019

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.05114

zbMATH Keywords

greatest common divisorlinear recurrencesnatural densities

Mathematics Subject Classification ID

Recurrences (11B37) Congruences; primitive roots; residue systems (11A07) Distribution of integers with specified multiplicative constraints (11N25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (3)

Greatest common divisors of shifted primes and Fibonacci numbers ⋮ On the greatest common divisor of n and the nth Fibonacci number, II ⋮ On terms in a dynamical divisibility sequence having a fixed g.c.d with their indices

Cites Work

• Diophantine equations with power sums and universal Hilbert sets
• Multiplicities of recurrence sequences
• Finiteness of integral values for the ratio of two linear recurrences
• An upper bound for the g.c.d. of \(a^n-1\) and \(b^n -1\)
• The moments of the logarithm of a G.C.D. related to Lucas sequences
• 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
• Distribution of integral values for the ratio of two linear recurrences
• On numbers \(n\) relatively prime to the \(n\)th term of a linear recurrence
• The Distribution of Self-Fibonacci Divisors
• On numbers n dividing the nth term of a linear recurrence
• On numbers n dividing the nth term of a Lucas sequence
• On primitive divisors of n² + b
• The terms in Lucas sequences divisible by their indices
• Torsion points on curves and common divisors of a^k-1 and b^k-1
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