{
  "id": "1407.5789",
  "version": "v1",
  "published": "2014-07-22T09:04:24.000Z",
  "updated": "2014-07-22T09:04:24.000Z",
  "title": "A Curious Congruence Involving Alternating Harmonic Sums",
  "authors": [
    "Liuquan Wang"
  ],
  "comment": "This is an original research article about congruences. It has submitted for publication in June 2014",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime and ${\\mathcal{P}_{p}}$ the set of positive integers which are prime to $p$. We establish the following interesting congruence \\[\\sum\\limits_{\\begin{smallmatrix} i+j+k={{p}^{r}} i,j,k\\in {\\mathcal{P}_{p}} \\end{smallmatrix}}{\\frac{{{(-1)}^{i}}}{ijk}}\\equiv \\frac{{{p}^{r-1}}}{2}{{B}_{p-3}}\\, (\\bmod \\, {{p}^{r}}).\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-22T09:04:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11A41"
    ],
    "keywords": [
      "alternating harmonic sums",
      "curious congruence",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5789W"
    }
  }
}