{
  "id": "1304.4361",
  "version": "v2",
  "published": "2013-04-16T08:34:58.000Z",
  "updated": "2015-04-07T20:32:45.000Z",
  "title": "On arithmetic progressions on Edwards curves",
  "authors": [
    "Enrique Gonzalez-Jimenez"
  ],
  "journal": "Acta Arithmetica 167 (2015), 117-132",
  "doi": "10.4064/aa167-2-2",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let m be a positive integer and a,q two rational numbers. Denote by AP_m(a,q) the set of rational numbers d such that a,a+q,...,a+(m-1)q form an arithmetic progression in the Edwards curve E_d:x^2+y^2=1+d x^2 y^2. We study the set AP_m(a,q) and we parametrize it by the rational points of an algebraic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-16T08:34:58.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-07T20:32:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G30",
      "11B25",
      "11D45",
      "14G05"
    ],
    "keywords": [
      "arithmetic progression",
      "edwards curve",
      "rational numbers",
      "algebraic curve"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.4361G"
    }
  }
}