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Primes Generated by Recurrence Sequences

G. Everest·S. Stevens·D. Tamsett·T. Ward
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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.

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G. Everest, S. Stevens, D. Tamsett, T. Ward. 2004-12-03. Primes Generated by Recurrence Sequences. https://arxiv.org/abs/math/0412079

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