{
  "id": "math/9906016",
  "version": "v3",
  "published": "1999-06-02T14:34:05.000Z",
  "updated": "1999-08-13T17:37:40.000Z",
  "title": "On periodic sequences for algebraic numbers",
  "authors": [
    "Thomas Garrity"
  ],
  "comment": "22 pages. An error in section five of the original paper has been corrected, resulting in some slight alterations in the statements in the theorems in section six",
  "categories": [
    "math.NT"
  ],
  "abstract": "For each positive integer n greater than or equal to 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n=2 case is equivalent to the standard continued fraction algorithm. For n=3, it reduces to a new iteration of the triangle. Cubic irrationals that are roots of x^3 + k x^2 + x - 1 are shown to be precisely those numbers with purely periodic expansions of period length one. For general positive integers n, it reduces to a new iteration of an n dimensional simplex.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-08-13T17:37:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70"
    ],
    "keywords": [
      "algebraic numbers",
      "periodic sequences",
      "standard continued fraction algorithm",
      "general positive integers",
      "period length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6016G"
    }
  }
}