{
  "id": "2309.11173",
  "version": "v1",
  "published": "2023-09-20T09:36:02.000Z",
  "updated": "2023-09-20T09:36:02.000Z",
  "title": "On Pillai's Problem involving Lucas sequences of the second kind",
  "authors": [
    "Sebastian Heintze",
    "Volker Ziegler"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider the Diophantine equation $ V_n - b^m = c $ for given integers $ b,c $ with $ b \\geq 2 $, whereas $ V_n $ varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions $ (n,m) $, then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of $ V_n $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-20T09:36:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second kind",
      "lucas sequences",
      "pillais problem",
      "diophantine equation",
      "lucas-lehmer sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}