Primitive divisors of elliptic divisibility sequences

Graham Everest, Gerard McLaren, Thomas Ward

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

{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.
Original languageEnglish
Pages (from-to)71-89
Number of pages19
JournalJournal of Number Theory
Volume118
Issue number1
DOIs
Publication statusPublished - 2006

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