Primitive divisors of elliptic divisibility sequences
By G. Everest, G. Mclaren, T. Ward. 2004
61 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2d1f1fe9c1535dc917a88760a6f2dc47717ddc6e
How researchers see this paper
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In Algebra and Number Theory
In Geometry and Topology
- Joseph H. Silverman
- T. Tucker
- Patrick Ingram
- K. Nguyen
- Chad Gratton
- Rafe Jones
- Shu Kawaguchi
- Robert L. Benedetto
In Mathematical Physics
- T. Tucker
- Patrick Ingram
- Joseph H. Silverman
- Franccois Berteloot
- Rafe Jones
- Shu Kawaguchi
- Robert L. Benedetto
Citations in the corpus
- Primitive divisors in arithmetic dynamics (2007, background): “This useful result has been extended and generalized in many ways, for example to more general linear recursions, to number fields, to elliptic curves, and to Drinfeld modules, see [6, 7, 9, 10, 12, 14, 15, 16, 21, 23, 25].”
- ABC implies primitive prime divisors in arithmetic dynamics (2012, background): “Much work has been done on this problem in the setting of elliptic curves (refer to [10, 15], for example).”