{
  "id": "2002.12136",
  "version": "v1",
  "published": "2020-02-24T18:36:30.000Z",
  "updated": "2020-02-24T18:36:30.000Z",
  "title": "On Diophantine equations over $\\mathbb Z[i]$ with $52$ unknowns",
  "authors": [
    "Yuri Matiyasevich",
    "Zhi-Wei Sun"
  ],
  "comment": "Submitted to Proc. of the 2019 Asian Logic Conf.; 5 pages",
  "categories": [
    "math.NT",
    "math.LO"
  ],
  "abstract": "In this paper we show that there is no algorithm to decide whether an arbitrarily given polynomial equation $P(z_1,\\ldots,z_{52})=0$ (with integer coefficients) over the Gaussian ring $\\mathbb Z[i]$ is solvable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-24T18:36:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D35",
      "11U05",
      "03D25",
      "11B39",
      "11D99",
      "11R11"
    ],
    "keywords": [
      "diophantine equations",
      "polynomial equation",
      "integer coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}