Primes Generated by Recurrence Sequences

Details Primes Generated by Recurrence Sequences Primes Generated by Recurrence Sequences

2004-12-03

arxiv.org/abs/math/0412079v2

Mathematics

Number Theory

Many small typos corrected; proof in Sect. 5 clarified; title changed

Scientific paper

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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