{
  "id": "1505.06500",
  "version": "v1",
  "published": "2015-05-24T23:27:49.000Z",
  "updated": "2015-05-24T23:27:49.000Z",
  "title": "On the greatest prime factor of some divisibility sequences",
  "authors": [
    "Amir Akbary",
    "Soroosh Yazdani"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $P(m)$ denote the greatest prime factor of $m$. For integer $a>1$, M. Ram Murty and S. Wong proved that, under the assumption of the ABC conjecture, $$P(a^n-1)\\gg_{\\epsilon, a} n^{2-\\epsilon}$$ for any $\\epsilon>0$. We study analogues results for the corresponding divisibility sequence over the function field $\\mathbb{F}_q(t)$ and for some divisibility sequences associated to elliptic curves over the rational field $\\mathbb{Q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-24T23:27:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11G05",
      "11J25"
    ],
    "keywords": [
      "greatest prime factor",
      "study analogues results",
      "ram murty",
      "rational field",
      "elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506500A"
    }
  }
}