{
  "id": "math/0401341",
  "version": "v1",
  "published": "2004-01-26T20:36:29.000Z",
  "updated": "2004-01-26T20:36:29.000Z",
  "title": "On the period of the continued fraction expansion of ${\\sqrt {2^{2n+1}+1}}$",
  "authors": [
    "Yann Bugeaud",
    "Florian Luca"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove that the period of the continued fraction expansion of ${\\sqrt {2^{n}+1}}$ tends to infinity when $n$ tends to infinity through odd positive integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-26T20:36:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11J25"
    ],
    "keywords": [
      "continued fraction expansion",
      "odd positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1341B"
    }
  }
}