{
  "id": "1906.06330",
  "version": "v1",
  "published": "2019-06-13T19:48:06.000Z",
  "updated": "2019-06-13T19:48:06.000Z",
  "title": "On the $x$--coordinates of Pell equations which are products of two Pell numbers",
  "authors": [
    "Mahadi Ddamulira"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:1905.11322",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $ \\{P_m\\}_{m\\ge 0} $ be the sequence of Pell numbers given by $ P_0=0, ~ P_1=1 $ and $ P_{m+2}=2P_{m+1}+P_m $ for all $ m\\ge 0 $. In this paper, for an integer $d\\geq 2$ which is square free, 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 product of two Pell numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-13T19:48:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11B39",
      "11J86"
    ],
    "keywords": [
      "pell numbers",
      "pell equation",
      "coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}