Primitive divisors of elliptic divisibility sequences

Everest, Graham, McLaren, Gerard and Ward, Thomas (2006) Primitive divisors of elliptic divisibility sequences. Journal of Number Theory, 118 (1). pp. 71-89.

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{Silverman proved the analogue of Zsigmondy's Theorem for elliptic divisibility sequences. For elliptic curves in global minimal form, it seems likely this result is true in a uniform manner. We present such a result for certain infinite families of curves and points. Our methods allow the first explicit examples of the elliptic Zsigmondy Theorem to be exhibited. As an application, we show that every term beyond the fourth of the Somos-4 sequence has a primitive divisor.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 09 Feb 2023 09:30
DOI: 10.1016/j.jnt.2005.08.002

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