{
  "id": "2108.10624",
  "version": "v1",
  "published": "2021-08-24T10:20:31.000Z",
  "updated": "2021-08-24T10:20:31.000Z",
  "title": "Trinomial coefficients and a determinant of Sun",
  "authors": [
    "Hai-Liang Wu",
    "Yue-Feng She",
    "He-Xia Ni"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, by using the tool of trinomial coefficients we study some determinant problems posed by Zhi-Wei Sun. For example, given any odd prime $p$ with $p\\equiv 2\\pmod 3$, we show that $2\\det[\\frac{1}{i^2-ij+j^2}]_{1\\le i,j\\le p-1}$ is a quadratic residue modulo $p$. This confirms a conjecture of Zhi-Wei Sun.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-24T10:20:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "trinomial coefficients",
      "zhi-wei sun",
      "quadratic residue modulo",
      "determinant problems",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}