{
  "id": "1508.05644",
  "version": "v1",
  "published": "2015-08-23T18:52:38.000Z",
  "updated": "2015-08-23T18:52:38.000Z",
  "title": "The class number one problem for the real quadratic fields $\\mathbb{Q}\\left(\\sqrt{(an)^2+4a}\\right)$",
  "authors": [
    "András Biró",
    "Kostadinka Lapkova"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We solve unconditionally the class number one problem for the $2$-parameter family of real quadratic fields $\\mathbb{Q}(\\sqrt{d})$ with square-free discriminant $d=(an)^2+4a$ for positive odd integers $a$ and $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-23T18:52:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real quadratic fields",
      "class number",
      "square-free discriminant",
      "positive odd integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150805644B"
    }
  }
}