{
  "id": "1605.03756",
  "version": "v1",
  "published": "2016-05-12T10:53:58.000Z",
  "updated": "2016-05-12T10:53:58.000Z",
  "title": "On $X$-coordinates of Pell equations which are repdigits",
  "authors": [
    "Bernadette Faye",
    "Florian Luca"
  ],
  "comment": "All comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $b\\ge 2$ be a given integer. In this paper, we show that there only finitely many positive integers $d$ which are not squares, such that the Pell equation $X^2-dY^2=1$ has two positive integer solutions $(X,Y)$ with the property that their $X$-coordinates are base $b$-repdigits. We also give an upper bound on the largest such $d$ in terms of $b$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-12T10:53:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45"
    ],
    "keywords": [
      "pell equation",
      "coordinates",
      "upper bound",
      "positive integer solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}