{
  "id": "1710.09755",
  "version": "v1",
  "published": "2017-10-26T15:28:26.000Z",
  "updated": "2017-10-26T15:28:26.000Z",
  "title": "On the divisibility of class numbers of quadratic fields and the solvability of Diophantine equations",
  "authors": [
    "Azizul Hoque",
    "Helen K. Saikia"
  ],
  "journal": "SeMA J. 73 (2016), no. 3, 213--217",
  "doi": "10.1007/s40324-016-0065-1",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we provide criteria for the insolvability of the Diophantine equation $x^2+D=y^n$. This result is then used to determine the class number of the quadratic field $\\mathbb{Q}(\\sqrt{-D})$. We also determine some criteria for the divisibility of the class number of the quadratic field $\\mathbb{Q}(\\sqrt{-D})$ and this result is then used to discuss the solvability of the Diophantine equation $x^2+D=y^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-26T15:28:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11D61",
      "11R41"
    ],
    "keywords": [
      "diophantine equation",
      "quadratic field",
      "class number",
      "divisibility"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}