{
  "id": "1005.3624",
  "version": "v1",
  "published": "2010-05-20T08:14:25.000Z",
  "updated": "2010-05-20T08:14:25.000Z",
  "title": "On Arithmetic Progressions in Recurrences - A new characterization of the Fibonacci sequence",
  "authors": [
    "Akos Pinter",
    "Volker Ziegler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic progressions is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-20T08:14:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B25",
      "11B39",
      "11J87"
    ],
    "keywords": [
      "fibonacci sequence",
      "three-term arithmetic progressions",
      "characterization",
      "unique binary recurrence",
      "general linear recurrences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.3624P"
    }
  }
}