{
  "id": "1108.1546",
  "version": "v1",
  "published": "2011-08-07T14:57:51.000Z",
  "updated": "2011-08-07T14:57:51.000Z",
  "title": "On divisibility of sums of Apery polynomials",
  "authors": [
    "Hao Pan"
  ],
  "comment": "This is a preliminary draft",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "For any positive integers $m$ and $\\alpha$, we prove that $$\\sum_{k=0}^{n-1}\\epsilon^k(2k+1)A_k^{(\\alpha)}(x)^m\\equiv0\\pmod{n}, $$ where $\\epsilon\\in\\{1,-1\\}$ and $$ A_n^{(\\alpha)}(x)=\\sum_{k=0}^n\\binom{n}{k}^{\\alpha}\\binom{n+k}{k}^{\\alpha}x^k.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-07T14:57:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B65",
      "11B83",
      "05A10"
    ],
    "keywords": [
      "apery polynomials",
      "divisibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1546P"
    }
  }
}