Primes generated by recurrence sequences

Everest, G, Stevens, S, Tamsett, Duncan and Ward, Tom (2007) Primes generated by recurrence sequences. American Mathematical Monthly, 114 (5). pp. 417-431. ISSN 1930-0972

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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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Number Theory (former - to 2017) Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.ams.org/mathscinet-getitem?mr...
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:44
Last Modified:	13 Oct 2025 08:31
URI:	https://ueaeprints.uea.ac.uk/id/eprint/19712
DOI:

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