{
  "id": "1101.5425",
  "version": "v2",
  "published": "2011-01-28T01:43:16.000Z",
  "updated": "2011-03-14T22:41:58.000Z",
  "title": "A Lower Bound for the Size of a Sum of Dilates",
  "authors": [
    "Zeljka Ljujic"
  ],
  "comment": "v2 Case $k=pq$ added",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $A$ be a subset of integers and let $2\\cdot A+k\\cdot A=\\{2a_1+ka_2 : a_1,a_2\\in A\\}$. Y. O. Hamidoune and J. Ru\\' e proved that if $k$ is an odd prime and $A$ a finite set of integers such that $|A|>8k^k$, then $|2\\cdot A+k\\cdot A|\\ge (k+2)|A|-k^2-k+2$. In this paper, we extend this result for the case when $k$ is a power of an odd prime and the case when $k$ is a product of two odd primes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-14T22:41:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "odd prime",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.5425L"
    }
  }
}