{
  "id": "1409.8514",
  "version": "v1",
  "published": "2014-09-30T12:19:34.000Z",
  "updated": "2014-09-30T12:19:34.000Z",
  "title": "Powers of two as sums of two $k-$Fibonacci numbers",
  "authors": [
    "Jhon J. Bravo",
    "Carlos A. Gómez",
    "Florian Luca"
  ],
  "comment": "15 pages, no figure (Submitted). arXiv admin note: text overlap with arXiv:1402.4085",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an integer $k\\geq 2$, let $(F_{n}^{(k)})_{n}$ be the $k-$Fibonacci sequence which starts with $0,\\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we search for powers of 2 which are sums of two $k-$Fibonacci numbers. The main tools used in this work are lower bounds for linear forms in logarithms and a version of the Baker--Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of \\cite{BL2} and \\cite{BL13}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-30T12:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "fibonacci numbers",
      "baker-davenport reduction method",
      "lower bounds",
      "paper continues",
      "fibonacci sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8514B"
    }
  }
}