{
  "id": "2301.01985",
  "version": "v1",
  "published": "2023-01-05T09:43:51.000Z",
  "updated": "2023-01-05T09:43:51.000Z",
  "title": "Power Reducibility and Congruences",
  "authors": [
    "Rong-Hua Wang",
    "Michael X. X. Zhong"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper, a criterion on the power reducibility of holonomic sequences is presented. As applications, we show Ap\\'ery numbers $A_k$ and the central Delannoy polynomials $D_k(z)$ are both power reducible and present series of congruences. For example, when $p>3$ is a prime, we find that for each $r\\in\\mathbb{N}$, there is a $p$-adic integer $c_r$ such that \\begin{equation*} \\sum_{k=0}^{p-1}(2k+1)^{2r+1}A_k\\equiv c_r p \\pmod {p^3}. \\end{equation*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-05T09:43:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power reducibility",
      "congruences",
      "central delannoy polynomials",
      "holonomic sequences",
      "apery numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}