{
  "id": "1307.5078",
  "version": "v2",
  "published": "2013-07-18T20:45:08.000Z",
  "updated": "2013-07-24T14:54:18.000Z",
  "title": "Powers in Lucas Sequences via Galois Representations",
  "authors": [
    "Jesse Silliman",
    "Isabel Vogt"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $u_n$ be a nondegenerate Lucas sequence. We generalize the results of Bugeaud, Mignotte, and Siksek, 2006 to give a systematic approach towards the problem of determining all perfect powers in any particular Lucas sequence. We then prove a general bound on admissible prime powers in a Lucas sequence assuming the Frey-Mazur conjecture on isomorphic mod $p$ Galois representations of elliptic curves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-24T14:54:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois representations",
      "nondegenerate lucas sequence",
      "elliptic curves",
      "perfect powers",
      "general bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.5078S"
    }
  }
}