{
  "id": "1905.01015",
  "version": "v1",
  "published": "2019-05-02T17:44:17.000Z",
  "updated": "2019-05-02T17:44:17.000Z",
  "title": "On the problem of Pillai with $k$--generalized Fibonacci numbers and powers of $3$",
  "authors": [
    "Mahadi Ddamulira",
    "Florian Luca"
  ],
  "comment": "20 pages. arXiv admin note: substantial text overlap with arXiv:1707.07519, arXiv:1803.10434, arXiv:1902.03491",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an integer $k\\geq 2$, let $\\{F^{(k)}_{n}\\}_{n\\geqslant 2-k}$ be the $ k$--generalized Fibonacci sequence which starts with $0, \\ldots, 0,1$ (a total of $k$ terms) and for which each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $ c $ with at least two representations as a difference between a $ k $-generalized Fibonacci number and a power of $ 3 $. This paper continues the previous work of the first author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-02T17:44:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "generalized fibonacci number",
      "generalized fibonacci sequence",
      "first author",
      "paper continues",
      "difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}