{
  "id": "2001.10265",
  "version": "v1",
  "published": "2020-01-28T11:10:41.000Z",
  "updated": "2020-01-28T11:10:41.000Z",
  "title": "On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences",
  "authors": [
    "Mahadi Ddamulira",
    "Florian Luca"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $r\\ge 1$ be an integer and ${\\bf U}:=(U_{n})_{n\\ge 0} $ be the Lucas sequence given by $U_0=0$, $U_1=1, $ and $U_{n+2}=rU_{n+1}+U_n$, for all $ n\\ge 0 $. In this paper, we show that there are no positive integers $r\\ge 3,~x\\ne 2,~n\\ge 1$ such that $U_n^x+U_{n+1}^x$ is a member of ${\\bf U}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-28T11:10:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "exponential diophantine equation",
      "lucas sequence",
      "consecutive terms",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}