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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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
UEA Research Groups: Faculty of Science > Research Groups > Number Theory (former - to 2017)
Faculty of Science > Research Groups > Algebra and Combinatorics
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Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:44
Last Modified: 16 May 2023 00:45

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