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

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
12 Downloads (Pure)


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 languageEnglish
Pages (from-to)271-289
Number of pages19
JournalProceedings of the Edinburgh Mathematical Society
Issue number2
Publication statusPublished - Jun 2012


  • linear recurrence
  • Lucas sequence
  • divisibility


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