{
  "id": "2005.09186",
  "version": "v1",
  "published": "2020-05-19T03:18:09.000Z",
  "updated": "2020-05-19T03:18:09.000Z",
  "title": "On an inverse problem in additive number theory",
  "authors": [
    "Min Tang",
    "Hongwei Xu"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For a set $A$, let $P(A)$ be the set of all finite subset sums of $A$. In this paper, for a sequence of integers $B=\\{1<b_1<b_2<\\cdots\\}$ and $3b_1+5\\leq b_2\\leq 6b_1+10$, we determine the critical value for $b_3$ such that there exists an infinite sequence $A$ of positive integers for which $P(A)=\\mathbb{N}\\setminus B$. This result shows that we partially solve the problem of Fang and Fang [`On an inverse problem in additive number theory', Acta Math. Hungar. 158(2019), 36-39].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-19T03:18:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "additive number theory",
      "inverse problem",
      "finite subset sums",
      "acta math",
      "infinite sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}