{
  "id": "1406.3113",
  "version": "v1",
  "published": "2014-06-12T04:04:24.000Z",
  "updated": "2014-06-12T04:04:24.000Z",
  "title": "Pairwise Relative Primality of Positive Integers",
  "authors": [
    "Jerry Hu"
  ],
  "categories": [
    "math.NT",
    "math.CO",
    "math.PR"
  ],
  "abstract": "Given a graph $G=(V,E)$ with $V=\\{1,2,...,k\\}$, the $k$ positive integers $a_1,a_2, ...,a_k$ are $G$-wise relatively prime if $(a_i, a_j)=1$ for $\\{i,j\\} \\in E$. In this note we consider the problem of finding the probability $A_G$ that k positive integers are $G$-wise relatively prime. As an application of our results, we solve the problems of finding probabilities that k positive integers have exact (or at least) r relatively prime pairs, which was proposed by P. Moree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-12T04:04:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive integers",
      "pairwise relative primality",
      "wise relatively prime",
      "relatively prime pairs",
      "probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3113H"
    }
  }
}