{
  "id": "2203.11457",
  "version": "v1",
  "published": "2022-03-22T04:44:23.000Z",
  "updated": "2022-03-22T04:44:23.000Z",
  "title": "On the Frobenius Coin Problem in Three Variables",
  "authors": [
    "Negin Bagherpour",
    "Amir Jafari",
    "Amin Najafi Amin"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "The Frobenius coin problem in three variables, for three positive relatively prime integers $a_1< a_2< a_3$ asks to find the largest number not representable as $a_1x_1+a_2x_2+a_3x_3$ with non-negative integer coefficients $x_1$, $x_2$ and $x_3$. In this article, we present a new algorithm to solve this problem that is faster and in our belief simpler than all existing algorithms and runs in $\\mbox{O}(\\log a_1)$ steps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-22T04:44:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "frobenius coin problem",
      "belief simpler",
      "positive relatively prime integers",
      "non-negative integer coefficients",
      "largest number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}