{
  "id": "2005.14466",
  "version": "v1",
  "published": "2020-05-29T09:27:13.000Z",
  "updated": "2020-05-29T09:27:13.000Z",
  "title": "Proof of a q-supercongruence conjectured by Guo and Schlosser",
  "authors": [
    "Long Li",
    "Su-Dan Wang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we confirm the following conjecture of Guo and Schlosser: for any odd integer $n>1$ and $M=(n+1)/2$ or $n-1$, $$ \\sum_{k=0}^{M}[4k-1]_{q^2}[4k-1]^2\\frac{(q^{-2};q^4)_k^4}{(q^4;q^4)_k^4}q^{4k}\\equiv (2q+2q^{-1}-1)[n]_{q^2}^4\\pmod{[n]_{q^2}^4\\Phi_n(q^2)}, $$ where $[n]=[n]_q=(1-q^n)/(1-q),(a;q)_0=1,(a;q)_k=(1-a)(1-aq)\\cdots(1-aq^{k-1})$ for $k\\geq 1$ and $\\Phi_n(q)$ denotes the $n$-th cyclotomic polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-29T09:27:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-supercongruence",
      "th cyclotomic polynomial",
      "odd integer",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}