{
  "id": "1610.04020",
  "version": "v1",
  "published": "2016-10-13T10:57:36.000Z",
  "updated": "2016-10-13T10:57:36.000Z",
  "title": "There is no Diophantine quintuple",
  "authors": [
    "Bo He",
    "Alain Togbè",
    "Volker Ziegler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A set of $m$ positive integers $\\{a_1, a_2, \\dots , a_m\\}$ is called a Diophantine $m$-tuple if $a_i a_j + 1$ is a perfect square for all $1 \\le i < j \\le m$. In 2004 Dujella proved that there is no Diophantine sextuple and that there are at most finitely many Diophantine quintuples. In particular, a folklore conjecture concerning Diophantine $m$-tuples states that no Diophantine quintuple exists at all. In this paper we prove this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T10:57:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine quintuple",
      "folklore conjecture concerning diophantine",
      "diophantine sextuple",
      "perfect square",
      "tuples states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}