{
  "id": "1108.4840",
  "version": "v1",
  "published": "2011-08-24T13:47:04.000Z",
  "updated": "2011-08-24T13:47:04.000Z",
  "title": "Congruences involving $\\binom{4k}{2k}$ and $\\binom{3k}k$",
  "authors": [
    "Zhi-Hong Sun"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $p$ be a prime greater than 3. In the paper we mainly determine $\\sum_{k=0}^{[p/4]}\\binom{4k}{2k}(-1)^k$, $\\sum_{k=0}^{[p/3]}\\binom{3k}k, \\sum_{k=0}^{[p/3]}\\binom{3k}k(-1)^k$ and $\\sum_{k=0}^{[p/3]}\\binom{3k}k(-3)^k$ modulo $p$, where $[x]$ is the greatest integer not exceeding $x$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-24T13:47:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B39",
      "11A15",
      "11E25",
      "05A19"
    ],
    "keywords": [
      "congruences",
      "prime greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4840S"
    }
  }
}