{
  "id": "1905.10704",
  "version": "v1",
  "published": "2019-05-26T00:35:12.000Z",
  "updated": "2019-05-26T00:35:12.000Z",
  "title": "Continued Fractions and Factoring",
  "authors": [
    "Michele Elia"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Legendre found that the continued fraction expansion of $\\sqrt N$ having odd period leads directly to an explicit representation of $N$ as the sum of two squares. Similarly, it is shown here that the continued fraction expansion of $\\sqrt N$ having even period directly produces a factor of a composite $N$. Shanks' infrastructural method is then revisited, and some consequences of its application to factorization by means of the continued fraction expansion of $\\sqrt N$ are derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-26T00:35:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continued fraction expansion",
      "explicit representation",
      "odd period",
      "period directly produces",
      "infrastructural method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}