{
  "id": "1312.5241",
  "version": "v1",
  "published": "2013-12-18T17:43:13.000Z",
  "updated": "2013-12-18T17:43:13.000Z",
  "title": "Non-extensibility of the pair $\\{1, 3\\}$ to a Diophantine quintuple in $\\mathbb{Z}\\left[\\sqrt{-d}\\right]$",
  "authors": [
    "Zrinka Franušić",
    "Dijana Kreso"
  ],
  "journal": "Journal of Combinatorics and Number Theory, Volume 3, (2011), 1--15",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that the Diophantine pair $\\{1, 3\\}$ can not be extended to a Diophantine quintuple in $\\mathbb{Z}\\left[\\sqrt{-2}\\right]$. This result completes the work of the first author and establishes non-extensibility of the Diophantine pair $\\{1, 3\\}$ to a Diophantine quintuple in $\\mathbb{Z}\\left[\\sqrt{-d}\\right]$ for all $d\\in \\mathbb{N}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-18T17:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09",
      "11R11"
    ],
    "keywords": [
      "diophantine quintuple",
      "diophantine pair",
      "first author"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5241F"
    }
  }
}