{
  "id": "1510.00812",
  "version": "v1",
  "published": "2015-10-03T12:59:25.000Z",
  "updated": "2015-10-03T12:59:25.000Z",
  "title": "Exact additive complements",
  "authors": [
    "Imre Z. Ruzsa"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A,B$ be sets of positive integers such that $A+B$ contains all but finitely many positive integers. S\\'ark\\\"ozy and Szemer\\'edi proved that if $ A(x)B(x)/x \\to 1$, then $A(x)B(x)-x \\to \\infty $. Chen and Fang considerably improved S\\'ark\\\"ozy and Szemer\\'edi's bound. We further improve their estimate and show by an example that our result is nearly best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-03T12:59:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13",
      "11B34"
    ],
    "keywords": [
      "exact additive complements",
      "positive integers",
      "szemeredis bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}