{
  "id": "1401.0493",
  "version": "v1",
  "published": "2014-01-02T18:14:02.000Z",
  "updated": "2014-01-02T18:14:02.000Z",
  "title": "Congruences for $q^{[p/8]}\\pmod p$ II",
  "authors": [
    "Zhi-Hong Sun"
  ],
  "comment": "28 pages. arXiv admin note: substantial text overlap with arXiv:1108.3027",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Bbb Z$ be the set of integers, and let $p$ be a prime of the form $4k+1$. Suppose $q\\in\\Bbb Z$, $2\\nmid q$, $p\\nmid q$, $p=c^2+d^2$, $c,d\\in\\Bbb Z$ and $c\\equiv 1\\pmod 4$. In this paper we continue to discuss congruences for $q^{[p/8]}\\pmod p$ and present new reciprocity laws, but we assume $4p=x^2+qy^2$ or $p=x^2+2qy^2$, where $[\\cdot]$ is the greatest integer function and $x,y\\in\\Bbb Z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-02T18:14:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A15",
      "11A07",
      "11E25"
    ],
    "keywords": [
      "congruences",
      "greatest integer function",
      "reciprocity laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0493S"
    }
  }
}