{
  "id": "math/9802122",
  "version": "v1",
  "published": "1998-02-27T14:36:14.000Z",
  "updated": "1998-02-27T14:36:14.000Z",
  "title": "Tiling the integers with translates of one finite set",
  "authors": [
    "Ethan M. Coven",
    "Aaron D. Meyerowitz"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "A set is said to tile the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a finite set to tile the integers. For sets of prime power size, it was solved by D. Newman [J. Number Theory 9 (1977), 107--111]. We solve it for sets of size having at most two prime factors. The conditions are always sufficient, but it is unknown whether they are necessary for all finite sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-02-27T14:36:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B45",
      "11B75",
      "20K01"
    ],
    "keywords": [
      "finite set",
      "translates",
      "prime factors",
      "number theory",
      "disjoint union"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......2122C"
    }
  }
}