{
  "id": "1009.6139",
  "version": "v1",
  "published": "2010-09-30T13:59:08.000Z",
  "updated": "2010-09-30T13:59:08.000Z",
  "title": "On the continued fraction expansion of the unique root in F(p) of the equation x^4+x^2-Tx-1:12=0 and other related hyperquadratic expansions",
  "authors": [
    "Alain Lasjaunias"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of degree 4 in characteristic p=13. This equation has an analogue for all primes p>=5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p modulo 3. We describe this pattern in the first case, considering especially p=7 and p=13. in the second case we only give indications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-30T13:59:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continued fraction expansion",
      "related hyperquadratic expansions",
      "unique root",
      "algebraic power series",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.6139L"
    }
  }
}