{
  "id": "1507.03485",
  "version": "v1",
  "published": "2015-07-13T14:59:11.000Z",
  "updated": "2015-07-13T14:59:11.000Z",
  "title": "On the number of representations of $n$ by $ax(x-1)/2+by(y-1)/2+cz(z-1)/2+dt(t-1)/2$",
  "authors": [
    "Min Wang",
    "Zhi-Hong Sun"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Bbb Z$ and $\\Bbb N$ be the set of integers and the set of positive integers, respectively. For $a,b,c,d,n\\in\\Bbb N$ let $t(a,b,c,d;n)$ be the number of representations of $n$ by $ax(x-1)/2+by(y-1)/2+cz(z-1)/2 +dt(t-1)/2$ $(x,y,z,t\\in\\Bbb Z$). In this paper we obtain explicit formulas for $t(a,b,c,d;n)$ in the cases $(a,b,c,d)=(1,1,4,4),\\ (1,4,4,4),\\ (1,2,2,4),\\ (1,2,4,4)$, $(1,1,9,9),\\ (1,9,9,9),\\ (1,1,1,9),\\ (1,3,9,9),\\ (1,1,3,9).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-13T14:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D85",
      "11E25"
    ],
    "keywords": [
      "representations",
      "explicit formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703485W"
    }
  }
}