{
  "id": "1311.0422",
  "version": "v2",
  "published": "2013-11-03T01:34:44.000Z",
  "updated": "2013-11-19T02:53:54.000Z",
  "title": "On the Sum of Dilations of a Set",
  "authors": [
    "Antal Balog",
    "George Shakan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that for any relatively prime integers $1\\leq p<q$ and for any finite $A \\subset \\mathbb{Z}$ one has $$|p \\cdot A + q \\cdot A | \\geq (p + q) |A| - (pq)^{(p+q-3)(p+q) + 1}.$$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-19T02:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75"
    ],
    "keywords": [
      "relatively prime integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0422B"
    }
  }
}