{
  "id": "1811.03015",
  "version": "v1",
  "published": "2018-11-02T19:29:20.000Z",
  "updated": "2018-11-02T19:29:20.000Z",
  "title": "An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers",
  "authors": [
    "Salah E. Rihane",
    "Bernadette Faye",
    "Florian Luca",
    "Alain Togbe"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T19:29:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "exponential diophantine equation",
      "consecutive balancing numbers",
      "difference",
      "positive integer variables",
      "th term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}