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On numbers n dividing the nth term of a linear recurrence

Part of: Sequences and sets Multiplicative number theory Elementary number theory

Published online by Cambridge University Press:  23 February 2012

Juan José Alba González ,
Florian Luca ,
Carl Pomerance  and
Igor E. Shparlinski
Juan José Alba González
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autonoma de México, CP 58089, Morelia, Michoacán, México (jjalba@gmail.com; fluca@matmor.unam.mx)
Florian Luca
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autonoma de México, CP 58089, Morelia, Michoacán, México (jjalba@gmail.com; fluca@matmor.unam.mx)
Carl Pomerance
Affiliation:
Mathematics Department, Dartmouth College, Hanover, NH 03755, USA (carl.pomerance@dartmouth.edu)
Igor E. Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia (igor.shparlinski@mq.edu.au)
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Abstract

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We give upper and lower bounds on the count of positive integers n ≤ x dividing the nth term of a non-degenerate linearly recurrent sequence with simple roots.

Keywords

linear recurrenceLucas sequencedivisibility

MSC classification

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

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 271 - 289
Copyright
Copyright © Edinburgh Mathematical Society 2012

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