{
  "id": "1708.03804",
  "version": "v1",
  "published": "2017-08-12T18:25:17.000Z",
  "updated": "2017-08-12T18:25:17.000Z",
  "title": "An Elliptic Curve Analogue to the Fermat Numbers",
  "authors": [
    "Skye Binegar",
    "Randy Dominick",
    "Meagan Kenney",
    "Jeremy Rouse",
    "Alex Walsh"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-12T18:25:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11B37",
      "11G15",
      "11Y11"
    ],
    "keywords": [
      "fermat numbers",
      "elliptic curve analogue",
      "arbitrary elliptic curves",
      "order universality",
      "specific curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}