{
  "id": "1909.13173",
  "version": "v1",
  "published": "2019-09-29T00:19:08.000Z",
  "updated": "2019-09-29T00:19:08.000Z",
  "title": "Proof of some supercongruences via the Wilf-Zeilberger method",
  "authors": [
    "Guo-Shuai Mao"
  ],
  "comment": "20 pages. This is a preliminary manuscript. Any comments are welcome",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, we prove some supercongruences via the Wilf-Zeilberger method. For instance, for any odd prime $p$ and positive integer $r$ and $\\delta\\in\\{1,2\\}$, we have \\begin{align*} \\sum_{n=0}^{(p^r-1)/\\delta} \\frac{\\left(\\frac12\\right)^5_n}{n!^5}(10n^2+6n+1)(-4)^n &\\equiv\\begin{cases}p^{2r}\\ \\pmod{p^{r+4}} &\\tt{if}\\ r\\leq4, \\\\0\\ \\pmod{p^{r+4}} &\\tt{if}\\ r \\geq5. \\end{cases} \\end{align*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-29T00:19:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wilf-zeilberger method",
      "supercongruences",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}