{
  "id": "1910.09983",
  "version": "v1",
  "published": "2019-10-20T01:45:58.000Z",
  "updated": "2019-10-20T01:45:58.000Z",
  "title": "Proof of two supercongruences conjectured by Z.-W. Sun via the Wilf-Zeilberger method",
  "authors": [
    "Guo-Shuai Mao"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1910.00779",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, we prove two supercongruences conjectured by Z.-W. Sun via the Wilf-Zeilberger method. One of them is, for any prime $p>3$, \\begin{align*} \\sum_{n=0}^{(p-1)/2}\\frac{6n+1}{(-512)^n}\\binom{2n}n^3&\\equiv p\\left(\\frac{-2}p\\right)+\\frac{p^3}4\\left(\\frac2p\\right)E_{p-3}\\pmod{p^4}, \\end{align*} where $\\left(\\frac{\\cdot}p\\right)$ stands for the Legendre symbol, and $E_{n}$ is the $n$-th Euler number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-20T01:45:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wilf-zeilberger method",
      "supercongruences",
      "th euler number",
      "legendre symbol"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}