{
  "id": "2005.12084",
  "version": "v1",
  "published": "2020-05-25T12:53:18.000Z",
  "updated": "2020-05-25T12:53:18.000Z",
  "title": "On the $p$-divisibility of class numbers of an infinite family of imaginary quadratic fields $\\mathbb{Q} (\\sqrt{d})$ and $\\mathbb{Q} (\\sqrt{d+1}).$",
  "authors": [
    "Pasupulati Sunil Kumar",
    "Srilakshmi Krishnamoorthy"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For any odd prime $p,$ we construct an infinite family of pairs of imaginary quadratic fields $\\mathbb{Q}(\\sqrt{d}),\\mathbb{Q}(\\sqrt{d+1})$ whose class numbers are both divisible by $p.$ One of our theorems settles Iizuka's conjecture for the case $n=1$ and $p >2.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-25T12:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R11"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "class numbers",
      "infinite family",
      "theorems settles iizukas conjecture",
      "divisibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}