{
  "id": "math/0404487",
  "version": "v1",
  "published": "2004-04-27T14:10:12.000Z",
  "updated": "2004-04-27T14:10:12.000Z",
  "title": "On Some Finite Sums with Factorials",
  "authors": [
    "Branko Dragovich"
  ],
  "comment": "10 pages",
  "journal": "FACTA UNIVERSITATIS; Ser. Math. Inform. 14 (1999) 1-10",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The summation formula $$ \\sum^{n-1}_{i=0}\\epsilon^i i! (i^k+u_k) = v_k+\\epsilon^{n-1} n! A_{k-1}(n) $$ $(\\epsilon=\\pm 1; k=1,2,...; u_k, v_k\\in \\msbm\\hbox{Z}; A_{k-1}$ is a polynomial) is derived and its various aspects are considered. In particular, divisibility with respect to $n$ is investigated. Infinitely many equivalents to Kurepa's hypothesis on the left factorial are found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-27T14:10:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05"
    ],
    "keywords": [
      "finite sums",
      "summation formula",
      "kurepas hypothesis",
      "left factorial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4487D"
    }
  }
}