{
  "id": "1806.10136",
  "version": "v1",
  "published": "2018-06-26T09:19:53.000Z",
  "updated": "2018-06-26T09:19:53.000Z",
  "title": "On the almost universality of $\\lfloor x^2/a\\rfloor+\\lfloor y^2/b\\rfloor+\\lfloor z^2/c\\rfloor$",
  "authors": [
    "Hai-Liang Wu",
    "He-Xia Ni",
    "Hao Pan"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1806.02105",
  "categories": [
    "math.NT"
  ],
  "abstract": "For each real number $r$, let $\\lfloor r\\rfloor$ denote the integral part of $r$. In this paper, with the help of congruence theta functions, we obtain the following results: (i) For each integer $m\\ge3$, every sufficiently large integer $n$ can be written as $$\\lfloor x^2/m\\rfloor+\\lfloor y^2/m\\rfloor+\\lfloor z^2/m\\rfloor,$$ with $x,y,z\\in\\Z$. (ii) For any integers $a,b,c\\ge5$, assume that $a,b,c$ are pairwisely coprime, then every sufficiently large integer $n$ can be written as $$\\lfloor x^2/a\\rfloor+\\lfloor y^2/b\\rfloor+\\lfloor z^2/c\\rfloor,$$ with $x,y,z\\in\\Z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-26T09:19:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficiently large integer",
      "universality",
      "congruence theta functions",
      "real number",
      "integral part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}