{
  "id": "math/0504569",
  "version": "v2",
  "published": "2005-04-28T12:56:42.000Z",
  "updated": "2006-08-11T12:37:09.000Z",
  "title": "Some Arithmetic Properties of the q-Euler Numbers and q-Salié Numbers",
  "authors": [
    "Victor J. W. Guo",
    "Jiang Zeng"
  ],
  "comment": "12 pages, see also http://math.univ-lyon1.fr/~guo",
  "journal": "European J. Combin. 27 (2006), 884--895",
  "doi": "10.1016/j.ejc.2005.04.009",
  "categories": [
    "math.CO"
  ],
  "abstract": "For m>n\\geq 0 and 1\\leq d\\leq m, it is shown that the q-Euler number E_{2m}(q) is congruent to q^{m-n}E_{2n}(q) mod (1+q^d) if and only if m\\equiv n mod d. The q-Sali\\'e number S_{2n}(q) is shown to be divisible by (1+q^{2r+1})^{\\left\\lfloor \\frac{n}{2r+1}\\right\\rfloor} for any r\\geq 0. Furthermore, similar congruences for the generalized q-Euler numbers are also obtained, and some conjectures are formulated.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-11T12:37:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "05A15",
      "11A07"
    ],
    "keywords": [
      "arithmetic properties",
      "q-salie number",
      "similar congruences",
      "generalized q-euler numbers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4569G"
    }
  }
}