{
  "id": "2207.11331",
  "version": "v1",
  "published": "2022-07-22T20:49:02.000Z",
  "updated": "2022-07-22T20:49:02.000Z",
  "title": "On Pillai's problem involving two linear recurrent sequences: Padovan and Fibonacci",
  "authors": [
    "Pagdame Tiebekabe",
    "Serge Adonsou"
  ],
  "journal": "Malaya J. Mat. 10(03)(2022)",
  "doi": "10.26637/mjm1003/003",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we find all integers $c$ having at least two representations as a difference between linear recurrent sequences. This problem is a pillai problem involving Padovan and Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-22T20:49:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86",
      "11D61"
    ],
    "keywords": [
      "linear recurrent sequences",
      "pillais problem",
      "baker-davenport reduction method",
      "main theorem",
      "diophantine approximation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}