Periodic solutions to some difference equations over the integers

John R Greene, Kate Niedzielski

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper, we investigate periodic integer solutions {an} to where r is a rational number. We show that solutions can only exist, if -1 ≤ r ≤ 1/2 and we give several infinite families of rs, for which the above recurrence has periodic solutions in the integers.

Original languageEnglish (US)
Pages (from-to)321-346
Number of pages26
JournalJournal of Difference Equations and Applications
Issue number4
StatePublished - Apr 1 2010


  • Difference equation
  • Fibonacci identities
  • Lucas numbers
  • Periodic solutions


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