{
  "id": "1305.0577",
  "version": "v1",
  "published": "2013-05-02T20:53:00.000Z",
  "updated": "2013-05-02T20:53:00.000Z",
  "title": "Squares and difference sets in finite fields",
  "authors": [
    "Christine Bachoc",
    "Imre Z. Ruzsa",
    "Mate Matolcsi"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "For infinitely many primes $p=4k+1$ we give a slightly improved upper bound for the maximal cardinality of a set $B\\subset \\ZZ_p$ such that the difference set $B-B$ contains only quadratic residues. Namely, instead of the \"trivial\" bound $|B|\\leq \\sqrt{p}$ we prove $|B|\\leq \\sqrt{p}-1$, under suitable conditions on $p$. The new bound is valid for approximately three quarters of the primes $p=4k+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-02T20:53:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "11T06"
    ],
    "keywords": [
      "difference set",
      "finite fields",
      "upper bound",
      "maximal cardinality",
      "quadratic residues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.0577B"
    }
  }
}