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Primitive divisors of elliptic divisibility sequences

2005; Elsevier BV; Volume: 118; Issue: 1 Linguagem: Inglês

10.1016/j.jnt.2005.08.002

1096-1658

Graham Everest, Gerard Mclaren, Thomas Ward,

Advanced Algebra and Geometry

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.