{
  "id": "2106.02895",
  "version": "v1",
  "published": "2021-06-05T13:38:14.000Z",
  "updated": "2021-06-05T13:38:14.000Z",
  "title": "On length of the period of the continued fraction of $n\\sqrt{d}$",
  "authors": [
    "Filip Gawron",
    "Tomasz Kobos"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For a given quadratic irrational $\\alpha$, let us denote by $D(\\alpha)$ the length of the periodic part of the continued fraction expansion of $\\alpha$. We prove that for a positive integer $d$, which is not a perfect square, the sequence $(D(n\\sqrt{d}))_{n=1}^{\\infty}$ has infinitely many limit points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-05T13:38:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55"
    ],
    "keywords": [
      "limit points",
      "quadratic irrational",
      "perfect square",
      "continued fraction expansion",
      "periodic part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}