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An Elliptic Curve Analogue to the Fermat Numbers

Number Theory 2019-02-06 v1

Abstract

The Fermat numbers have many notable properties, including order universality, coprimality, and definition by a recurrence relation. We use arbitrary elliptic curves and rational points of infinite order to generate sequences that are analogous to the Fermat numbers. We demonstrate that these sequences have many of the same properties as the Fermat numbers, and we discuss results about the prime factors of sequences generated by specific curves and points.

Keywords

Cite

@article{arxiv.1708.03804,
  title  = {An Elliptic Curve Analogue to the Fermat Numbers},
  author = {Skye Binegar and Randy Dominick and Meagan Kenney and Jeremy Rouse and Alex Walsh},
  journal= {arXiv preprint arXiv:1708.03804},
  year   = {2019}
}

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24 pages