{
  "id": "1210.0881",
  "version": "v1",
  "published": "2012-10-02T19:04:22.000Z",
  "updated": "2012-10-02T19:04:22.000Z",
  "title": "A Class of Permutation Binomials over Finite Fields",
  "authors": [
    "Xiang-dong Hou"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $q>2$ be a prime power and $f={\\tt x}^{q-2}+t{\\tt x}^{q^2-q-1}$, where $t\\in\\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\\equiv 1\\pmod 4$; (ii) $t=-3$, $q\\equiv \\pm1\\pmod{12}$; (iii) $t=3$, $q\\equiv -1\\pmod 6$. We confirm this conjecture in the present paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-02T19:04:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T55",
      "33C05"
    ],
    "keywords": [
      "permutation binomials",
      "finite fields",
      "conjecture",
      "prime power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0881H"
    }
  }
}