Primes generated by recurrence sequences

G Everest, S Stevens, Duncan Tamsett, Tom Ward

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We consider primitive divisors of terms of integer sequences defined by quadratic polynomials. Apart from some small counterexamples, when a term has a primitive divisor, that primitive divisor is unique. It seems likely that the number of terms with a primitive divisor has a natural density. We discuss two heuristic arguments to suggest a value for that density, one using recent advances made about the distribution of roots of polynomial congruences.
Original languageEnglish
Pages (from-to)417-431
Number of pages15
JournalAmerican Mathematical Monthly
Volume114
Issue number5
Publication statusPublished - 2007

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