{
  "id": "2011.01658",
  "version": "v1",
  "published": "2020-11-03T12:19:41.000Z",
  "updated": "2020-11-03T12:19:41.000Z",
  "title": "Numbers represented by restricted sums of four squares",
  "authors": [
    "Guang-Liang Zhou",
    "Yue-Feng She"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove some results of restricted sums of four squares using arithmetic of quaternions in the ring of Lipschitz integers. For example, we show that every nonnegative integer $n$ can be written as $x^{2}+y^{2}+z^{2}+t^{2}$ where $x,y,z,t$ are integers and $x+y+2z+2t$ is a square or a cube.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-03T12:19:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "restricted sums",
      "lipschitz integers",
      "quaternions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}