{
  "id": "0811.1311",
  "version": "v2",
  "published": "2008-11-09T03:14:02.000Z",
  "updated": "2009-10-29T22:48:15.000Z",
  "title": "Squares in sumsets",
  "authors": [
    "Hoi Nguyen",
    "Van Vu"
  ],
  "comment": "33 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "A finite set $A$ of integers is square-sum-free if there is no subset of $A$ sums up to a square. In 1986, Erd\\H os posed the problem of determining the largest cardinality of a square-sum-free subset of $\\{1, ..., n \\}$. Answering this question, we show that this maximum cardinality is of order $n^{1/3+o(1)}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-29T22:48:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite set",
      "largest cardinality",
      "square-sum-free subset",
      "maximum cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1311N"
    }
  }
}