{
  "id": "1503.00637",
  "version": "v1",
  "published": "2015-03-02T17:46:07.000Z",
  "updated": "2015-03-02T17:46:07.000Z",
  "title": "Parametric solutions of Pell equations",
  "authors": [
    "Leonardo Zapponi"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "This short paper is concerned with polynomial Pell equations \\[P^2-DQ^2=1,\\] with $P,Q,D\\in\\Bbb C[X]$ and ${deg}(D)=2$. The main result shows that the polynomials $P$ and $Q$ are closely related to Chebyshev polynomials. We then investigate the existence of such polynomials in $\\Bbb Z[X]$ specializing to fixed solutions of ordinary Pell equations over the integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-02T17:46:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parametric solutions",
      "polynomial pell equations",
      "ordinary pell equations",
      "chebyshev polynomials",
      "short paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}