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Primitive divisors of elliptic divisibility sequences.

Everest, G. and McLaren, G. and Ward, T. (2006) 'Primitive divisors of elliptic divisibility sequences.', Journal of number theory., 118 (1). pp. 71-89.


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
Keywords:Elliptic curve, Primitive divisor, Zsigmondy's Theorem, Somos sequence, Elliptic divisibility sequence, Prime.
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Journal of number theory. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of number theory, 118/7, 2006, 10.1016/j.jnt.2005.08.002
Record Created:12 Oct 2012 12:05
Last Modified:16 Oct 2012 10:08

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