{
  "id": "2004.12122",
  "version": "v1",
  "published": "2020-04-25T12:23:11.000Z",
  "updated": "2020-04-25T12:23:11.000Z",
  "title": "On some congruences using multiple harmonic sums of length three and four",
  "authors": [
    "Walid Kehila"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In the present paper, we determine the sums $\\sum_{j=1}^{p-1}\\frac{H_j^{(s_1)}H_j^{(s_3)}}{j^{s_2}}$ and $\\sum_{j=1}^{p-1}\\frac{H_j^{(s_1)}H_j^{(s_3)}H_j^{(s_4)}}{j^{s_2}}$ modulo $p$ and modulo $p^2$ in certain cases. This is done by using multiple harmonic sums of length three and four, as well as, many other results. In addition, We recover three congruences conjectured by Z.-W Sun and solved later by the author himself and R. Me\\v{s}trovi\\'c.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-25T12:23:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B68",
      "11B50",
      "11B83"
    ],
    "keywords": [
      "multiple harmonic sums",
      "congruences",
      "author himself"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}