{
  "id": "1902.03491",
  "version": "v1",
  "published": "2019-02-09T21:18:27.000Z",
  "updated": "2019-02-09T21:18:27.000Z",
  "title": "On a problem of Pillai with Fibonacci numbers and powers of $3$",
  "authors": [
    "Mahadi Ddamulira"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Consider the sequence $ \\{F_{n}\\}_{n\\geq 0} $ of Fibonacci numbers defined by $ F_0=0 $, $ F_1 =1$ and $ F_{n+2}=F_{n+1}+ F_{n} $ for all $ n\\geq 0 $. In this paper, we find all integers $ c $ having at least two representations as a difference between a Fibonacci number and a power of $ 3 $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-09T21:18:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "fibonacci number",
      "representations",
      "difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}