{
  "id": "math/0601026",
  "version": "v1",
  "published": "2006-01-02T16:25:00.000Z",
  "updated": "2006-01-02T16:25:00.000Z",
  "title": "A remark on Zoloterav's theorem",
  "authors": [
    "Hao Pan"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of gamma_{a,n} coincides with the Jacobi symbol (a/n) if n=1 mod 4, and 1 if n=3 mod 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-02T16:25:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11A15"
    ],
    "keywords": [
      "zoloteravs theorem",
      "jacobi symbol",
      "odd integer",
      "permutation",
      "nonnegative residue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1026P"
    }
  }
}