{
  "id": "1612.09546",
  "version": "v1",
  "published": "2016-12-30T17:50:30.000Z",
  "updated": "2016-12-30T17:50:30.000Z",
  "title": "On the $X$-coordinates of Pell equations which are Tribonacci numbers",
  "authors": [
    "Florian Luca",
    "Amanda Montejano",
    "Laszlo Szalay",
    "Alain Togbé"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an integer $d\\geq 2$ which is not a square, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=\\pm 1$ which is a Tribonacci number, with a few exceptions that we completely characterize.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-30T17:50:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11B39",
      "11J86"
    ],
    "keywords": [
      "pell equation",
      "tribonacci number",
      "coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}