{
  "id": "1402.4085",
  "version": "v1",
  "published": "2014-02-17T17:56:33.000Z",
  "updated": "2014-02-17T17:56:33.000Z",
  "title": "Coincidences in generalized Lucas sequences",
  "authors": [
    "Eric F. Bravo",
    "Jhon J. Bravo",
    "Florian Luca"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an integer $k\\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\\ell)}$ in nonnegative integers $n,k,m,\\ell$ with $k, \\ell\\geq 2$. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method. This paper is a continuation of the earlier work [4].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-17T17:56:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "generalized lucas sequence",
      "coincidences",
      "baker-davenport reduction method",
      "main theorem",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4085B"
    }
  }
}