Primes Generated by Recurrence Sequences
Number Theory
2013-05-28 v2
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.
Cite
@article{arxiv.math/0412079,
title = {Primes Generated by Recurrence Sequences},
author = {G. Everest and S. Stevens and D. Tamsett and T. Ward},
journal= {arXiv preprint arXiv:math/0412079},
year = {2013}
}
Comments
Many small typos corrected; proof in Sect. 5 clarified; title changed