{
  "id": "2204.10132",
  "version": "v1",
  "published": "2022-04-21T14:35:41.000Z",
  "updated": "2022-04-21T14:35:41.000Z",
  "title": "Supercongruences for sums involving $\\binom ak^m$",
  "authors": [
    "Zhi-Hong Sun"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $p$ be an odd prime, and let $a$ be a rational $p$-adic integer with $a\\not\\equiv 0\\pmod p$. In this paper, using WZ method we establish the congruences for $\\sum_{k=0}^{p-1} \\binom ak^2(-1)^k(1-\\frac 2ak)$ modulo $p^2$ and $\\sum_{k=0}^{p-1} \\binom ak^r(1-\\frac 2ak)^s$ modulo $p^4$, where $r\\in\\{3,4\\}$ and $s\\in\\{1,3\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-21T14:35:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "05A19",
      "11B65",
      "11B68",
      "11E25"
    ],
    "keywords": [
      "supercongruences",
      "wz method",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}