{
  "id": "math/0505128",
  "version": "v9",
  "published": "2005-05-09T15:54:48.000Z",
  "updated": "2007-03-08T14:26:35.000Z",
  "title": "Mixed sums of squares and triangular numbers",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "11 pages",
  "journal": "Acta Arith. 127(2007), no.2, 103-113",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "By means of $q$-series, we prove that any natural number is a sum of an even square and two triangular numbers, and that each positive integer is a sum of a triangular number plus $x^2+y^2$ for some integers $x$ and $y$ with $x\\not\\equiv y (mod 2)$ or $x=y>0$. The paper also contains some other results and open conjectures on mixed sums of squares and triangular numbers.",
  "revisions": [
    {
      "version": "v9",
      "updated": "2007-03-08T14:26:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25",
      "05A30",
      "11B65",
      "11D85",
      "11P99"
    ],
    "keywords": [
      "mixed sums",
      "triangular number plus",
      "natural number",
      "open conjectures",
      "positive integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5128S"
    }
  }
}