{
  "id": "1302.5991",
  "version": "v9",
  "published": "2013-02-25T04:11:02.000Z",
  "updated": "2015-01-09T12:23:30.000Z",
  "title": "New Results for Sorli's Conjecture on Odd Perfect Numbers",
  "authors": [
    "Jose Arnaldo B. Dris"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $N={q^k}{n^2}$ is an odd perfect number given in Eulerian form, then Sorli's conjecture predicts that $k=1$. In this article, we give a strategy for trying to prove that the inequality $n < q$ is equivalent to this conjecture. We conclude with some remaining open questions regarding $k$ and a conjectured relationship between the divisors $q^k$ and $n$.",
  "revisions": [
    {
      "version": "v8",
      "updated": "2013-10-04T06:53:42.000Z",
      "abstract": "If $N={q^k}{n^2}$ is an odd perfect number given in Eulerian form, then Sorli's conjecture predicts that $k=\\nu_{q}(N)=1$. In this article, we give a strategy for trying to prove that the inequality $n < q$ is equivalent to this conjecture. We conclude with some remaining open questions regarding $k$ and a conjectured relationship between the components $q^k$ and $n$.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v9",
      "updated": "2015-01-09T12:23:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11J25",
      "11J99"
    ],
    "keywords": [
      "odd perfect number",
      "sorlis conjecture predicts",
      "eulerian form",
      "inequality",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.5991D"
    }
  }
}