{
  "id": "2205.13168",
  "version": "v1",
  "published": "2022-05-26T05:41:11.000Z",
  "updated": "2022-05-26T05:41:11.000Z",
  "title": "On the Exponential Diophantine Equation $(F_{m+1}^{(k)})^x-(F_{m-1}^{(k)})^x = F_n^{(k)}$",
  "authors": [
    "Hayat Bensella",
    "Bijan Kumar Patel",
    "Djilali Behloul"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we explicitly find all solutions of the title Diophantine equation, using lower bounds for linear forms in logarithms and properties of continued fractions. Further, we use a version of the Baker-Davenport reduction method in Diophantine approximation, due to Dujella and Peth\\\"o. This paper extends the previous work of \\cite{Patel}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-26T05:41:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86",
      "11D61"
    ],
    "keywords": [
      "exponential diophantine equation",
      "title diophantine equation",
      "baker-davenport reduction method",
      "linear forms",
      "paper extends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}