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Primes Generated by Recurrence Sequences

2007; Taylor & Francis; Volume: 114; Issue: 5 Linguagem: Inglês

10.1080/00029890.2007.11920430

1930-0972

Graham Everest, Shaun Stevens, D. Tamsett, Thomas Ward,

Coding theory and cryptography

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.