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)

23 Downloads (Pure)

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.\}",

year = "2012",

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AU - González, Juan José Alba

AU - Luca, Florian

AU - Pomerance, Carl

AU - Shparlinski, Igor E.

PY - 2012/6

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N2 - 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.

AB - 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.

KW - linear recurrence

KW - Lucas sequence

KW - divisibility

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DO - 10.1017/S0013091510001355

M3 - Article

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SP - 271

EP - 289

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 2

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On numbers n dividing the nth term of a linear recurrence

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Keywords

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