{
  "id": "math/0502187",
  "version": "v4",
  "published": "2005-02-09T20:21:42.000Z",
  "updated": "2007-08-05T00:00:37.000Z",
  "title": "Congruences for sums of binomial coefficients",
  "authors": [
    "Zhi-Wei Sun",
    "Roberto Tauraso"
  ],
  "journal": "J. Number Theory 126(2007), no.2, 287-296",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let q>1 and m>0 be relatively prime integers. We find an explicit period $\\nu_m(q)$ such that for any integers n>0 and r we have $[n+\\nu_m(q),r]_m(a)=[n,r]_m(a) (mod q)$ whenever a is an integer with $\\gcd(1-(-a)^m,q)=1$, or a=-1 (mod q), or a=1 (mod q) and 2|m, where $[n,r]_m(a)=\\sum_{k=r(mod m)}\\binom{n}{k}a^k$. This is a further extension of a congruence of Glaisher.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-08-05T00:00:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "05A10",
      "11A07"
    ],
    "keywords": [
      "binomial coefficients",
      "congruence",
      "relatively prime integers",
      "explicit period"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2187S"
    }
  }
}