{
  "id": "math/0505187",
  "version": "v5",
  "published": "2005-05-10T19:16:26.000Z",
  "updated": "2007-12-24T15:34:14.000Z",
  "title": "Mixed sums of squares and triangular numbers (II)",
  "authors": [
    "Song Guo",
    "Hao Pan",
    "Zhi-Wei Sun"
  ],
  "journal": "Integers 7(2007), A56, 5 pp",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "For an integer $x$ let $t_x$ denote the triangular number $x(x+1)/2$. Following a recent work of Z. W. Sun, we show that every natural number can be written in any of the following forms with $x,y,z\\in\\Z$: $$x^2+3y^2+t_z, x^2+3t_y+t_z, x^2+6t_y+t_z, 3x^2+2t_y+t_z, 4x^2+2t_y+t_z.$$ This confirms a conjecture of Sun.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-12-24T15:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25",
      "11D85",
      "11P99"
    ],
    "keywords": [
      "triangular number",
      "mixed sums",
      "natural number",
      "conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5187G"
    }
  }
}