{
  "id": "1411.6963",
  "version": "v1",
  "published": "2014-11-14T01:53:32.000Z",
  "updated": "2014-11-14T01:53:32.000Z",
  "title": "On certain quaternary quadratic forms",
  "authors": [
    "Kazuhide Matsuda"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we determine all the positive integers $a, b$ and $c$ such that every nonnegative integer can be represented as $$ f^{a,b}_c(x,y,z,w)=ax^2+by^2+c(z^2+zw+w^2) \\,\\, \\textrm{with} \\,\\,x,y,z,w\\in\\mathbb{Z}. $$ Furthermore, we prove that $f^{a,b}_c$ can represent all the nonnegative integers if it represents $n=1,2,3,5,6,10.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-14T01:53:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K25",
      "11E25"
    ],
    "keywords": [
      "quaternary quadratic forms",
      "nonnegative integer",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6963M"
    }
  }
}