On numbers n dividing the nth term of a linear recurrence

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

doi:10.1017/S0013091510001355

On numbers n dividing the nth term of a linear recurrence

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

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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Abstract

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.

Original language	English
Pages (from-to)	271-289
Number of pages	19
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	55
Issue number	2
DOIs	https://doi.org/10.1017/S0013091510001355
Publication status	Published - Jun 2012

Keywords

linear recurrence
Lucas sequence
divisibility

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title = "On numbers n dividing the nth term of a linear recurrence",

abstract = "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 recurrence, Lucas sequence, divisibility",

author = "Gonz{\'a}lez, {Juan Jos{\'e} Alba} and Florian Luca and Carl Pomerance and Shparlinski, {Igor E.}",

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AU - Pomerance, Carl

AU - Shparlinski, Igor E.

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KW - divisibility

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On numbers n dividing the nth term of a linear recurrence

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Keywords

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