{
  "id": "0912.1280",
  "version": "v5",
  "published": "2009-12-07T19:58:20.000Z",
  "updated": "2009-12-14T20:06:57.000Z",
  "title": "Congruences involving binomial coefficients and Lucas sequences",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "23 pages. The current Th. 1.4 is new",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper we obtain some congruences involving central binomial coefficients and Lucas sequences. For example, we show that if p>5 is a prime then $\\sum_{k=0}^{p-1}F_k*binom(2k,k)/12^k$ is congruent to 0,1,-1 modulo p according as p=1,4 (mod 5), p=13,17 (mod 30), and p=7,23 (mod 30) respectively, where {F_n} is the Fibonacci sequence. We also raise several conjectures.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2009-12-14T20:06:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "11A07",
      "11B39",
      "05A10"
    ],
    "keywords": [
      "lucas sequences",
      "congruences",
      "central binomial coefficients",
      "fibonacci sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1280S"
    }
  }
}