{
  "id": "1910.14365",
  "version": "v1",
  "published": "2019-10-31T10:52:25.000Z",
  "updated": "2019-10-31T10:52:25.000Z",
  "title": "On a system of difference equations of third order solved in closed form",
  "authors": [
    "Youssouf Akrour",
    "Nouressadat Touafek",
    "Yacine Halim"
  ],
  "comment": "Manuscript submitted to a journal for publication on 20.08.2019",
  "categories": [
    "math.DS",
    "nlin.SI"
  ],
  "abstract": "In this note we show the the system of difference equations $$ x_{n+1}=\\dfrac{ay_{n-2}x_{n-1}y_n+bx_{n-1}y_{n-2}+cy_{n-2}+d}{y_{n-2}x_{n-1}y_n},$$ $$y_{n+1}=\\dfrac{ax_{n-2}y_{n-1}x_n+by_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n-2}y_{n-1}x_n},$$ where $n\\in \\mathbb{N}_{0}$, the initial values $x_{-2}$, $x_{-1}$, $x_0$, $y_{-2}$, $y_{-1}$ and $y_0$ are arbitrary nonzero real numbers and the parameters $a$, $b$, $c$ and $d$ are arbitrary real numbers with $d\\ne 0$, can be solved in a closed form. We will see that when $a=b=c=d=1$ the solutions are expressed using the famous Teteranacci numbers. In particular, the results obtained here extend those in our work \\cite{arxiv}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-31T10:52:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A10",
      "40A05"
    ],
    "keywords": [
      "difference equations",
      "closed form",
      "third order",
      "arbitrary nonzero real numbers",
      "arbitrary real numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}