{
  "id": "1912.08070",
  "version": "v1",
  "published": "2019-12-15T14:55:27.000Z",
  "updated": "2019-12-15T14:55:27.000Z",
  "title": "Proof of a supercongruence conjectured by Sun through a $q$-microscope",
  "authors": [
    "Victor J. W. Guo"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Recently, Z.-W. Sun made the following conjecture: for any odd prime $p$ and odd integer $m$, $$ \\frac{1}{m^2{m-1\\choose (m-1)/2}}\\Bigg(\\sum_{k=0}^{(pm-1)/2}\\frac{{2k\\choose k}}{8^k} -\\left(\\frac{2}{p}\\right)\\sum_{k=0}^{(m-1)/2}\\frac{{2k\\choose k}}{8^k}\\Bigg) \\equiv 0\\pmod{p^2}. $$ In this note, applying the \"creative microscoping\" method, introduced by the author and Zudilin, we confirm the above conjecture of Sun.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-15T14:55:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "11A07",
      "11B65"
    ],
    "keywords": [
      "microscope",
      "supercongruence",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}