{
  "id": "2011.02757",
  "version": "v1",
  "published": "2020-11-05T10:59:36.000Z",
  "updated": "2020-11-05T10:59:36.000Z",
  "title": "Extension of a conjectural supercongruence of (G.3) of Swisher using Zeilberger's algorithm",
  "authors": [
    "Arijit Jana",
    "Gautam Kalita"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using Zeilberger's algorithm, we here give a proof of the supercongruence $$ \\sum_{n=0}^{\\frac{p^r-3}{4}}(8n+1)\\frac{\\left(\\frac{1}{4}\\right)_n^4}{(1)_n^4}\\equiv -p^3 \\sum_{n=0}^{\\frac{p^{r-2}-3}{4}}(8n+1)\\frac{\\left(\\frac{1}{4}\\right)_n^4}{(1)_n^4} ~~(\\text{mod }p^{\\frac{3r-1}{2}}),$$ for any odd integer $r>3$. This extends the third conjectural supercongruence of (G.3) of Swisher to modulo higher prime powers than that expected by Swisher.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-05T10:59:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y55",
      "11A07",
      "11B65",
      "40G99"
    ],
    "keywords": [
      "zeilbergers algorithm",
      "modulo higher prime powers",
      "third conjectural supercongruence",
      "odd integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}