{
  "id": "2108.06804",
  "version": "v1",
  "published": "2021-08-15T19:49:52.000Z",
  "updated": "2021-08-15T19:49:52.000Z",
  "title": "On a question of Mendès France on normal numbers",
  "authors": [
    "Verónica Becher",
    "Manfred G. Madritsch"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In 2008 or earlier, Michel Mend\\`es France asked for an instance of a real number $x$ such that both $x$ and $1/x$ are simply normal to a given integer base $b$. We give a positive answer to this question by constructing a number $x$ such that both $x$ and its reciprocal $1/x$ are continued fraction normal as well as normal to all integer bases greater than or equal to $2$. Moreover, $x$ and $1/x$ are both computable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-15T19:49:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K16",
      "11J70"
    ],
    "keywords": [
      "mendès france",
      "normal numbers",
      "integer bases greater",
      "continued fraction normal",
      "real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}