{
  "id": "2206.10356",
  "version": "v1",
  "published": "2022-06-14T20:44:14.000Z",
  "updated": "2022-06-14T20:44:14.000Z",
  "title": "Sums of Fibonacci numbers close to a power of 2",
  "authors": [
    "Elchin Hasanalizade"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella-Peth\\\"{o} version of the Baker-Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of Chern and Cui.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-14T20:44:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "fibonacci numbers close",
      "lucas numbers close",
      "baker-davenport reduction method",
      "lower bounds",
      "linear forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}