{
  "id": "1508.02106",
  "version": "v1",
  "published": "2015-08-10T02:11:13.000Z",
  "updated": "2015-08-10T02:11:13.000Z",
  "title": "Searching for Diophantine quintuples",
  "authors": [
    "Mihai Cipu",
    "Tim Trudgian"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider Diophantine quintuples $\\{a, b, c, d, e\\}$. These are sets of distinct positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $1.18\\cdot 10^{27}$ Diophantine quintuples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-10T02:11:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09",
      "11D45",
      "11J86"
    ],
    "keywords": [
      "diophantine quintuples",
      "distinct positive integers",
      "perfect square",
      "current estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150802106C"
    }
  }
}