{
  "id": "1008.1274",
  "version": "v1",
  "published": "2010-08-06T20:19:09.000Z",
  "updated": "2010-08-06T20:19:09.000Z",
  "title": "On divisors of Lucas and Lehmer numbers",
  "authors": [
    "C. L. Stewart"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let u(n) be the n-th term of a Lucas sequence or a Lehmer sequence.In this article we shall establish an estimate from below for the greatest prime factor of u(n) which is of the form nexp(logn/104loglogn). In so doing we are able to resolve a question of Schinzel from 1962 and a conjecture of Erdos from 1965.In addition we are able to give the first general improvement on results of Bang from 1886 and Carmichael from 1912.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-06T20:19:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "lehmer numbers",
      "greatest prime factor",
      "first general improvement",
      "lehmer sequence",
      "n-th term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1274S"
    }
  }
}