{
  "id": "2103.14861",
  "version": "v1",
  "published": "2021-03-27T09:38:16.000Z",
  "updated": "2021-03-27T09:38:16.000Z",
  "title": "Continued Fractions, Quadratic Fields, and Factoring: Some Computational Aspects",
  "authors": [
    "Michele Elia"
  ],
  "comment": "8 pages, to appear on Collectio Cyphrarum. arXiv admin note: text overlap with arXiv:1905.10704",
  "categories": [
    "math.NT"
  ],
  "abstract": "Legendre discovered 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. In this vein, it was recently observed that the continued fraction expansion of $\\sqrt N$ having even period directly produces a factor of composite $N$. It is proved here that these apparently fortuitous occurrences allow us to propose and apply a variation of Shanks' infrastructural method which significantly reduces the asymptotic computational burden with respect to currently used factoring techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-27T09:38:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55",
      "11A51"
    ],
    "keywords": [
      "quadratic fields",
      "computational aspects",
      "continued fraction expansion",
      "asymptotic computational burden",
      "period directly produces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}