{
  "id": "2003.14221",
  "version": "v1",
  "published": "2020-03-30T08:57:43.000Z",
  "updated": "2020-03-30T08:57:43.000Z",
  "title": "On a supercongruence conjecture of Z.-W. Sun",
  "authors": [
    "Guo-Shuai Mao"
  ],
  "comment": "10 pages. arXiv admin note: text overlap with arXiv:2003.09810",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, we prove a supercongruence conjectured by Z.-W. Sun in 2013. The conjecture states that: Let $p$ be an odd prime and let $a\\in\\mathbb{Z}^{+}$. Then if $p\\equiv1\\pmod3$ or $a>1$, we have \\begin{align*} \\sum_{k=0}^{\\lfloor\\frac{5}6p^a\\rfloor}\\frac{\\binom{2k}k}{16^k}\\equiv\\left(\\frac{3}{p^a}\\right)\\pmod{p^2}, \\end{align*} where $\\left(\\frac{\\cdot}{\\cdot}\\right)$ is the Jacobi symbol.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-30T08:57:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supercongruence conjecture",
      "conjecture states",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}