{
  "id": "1206.4174",
  "version": "v1",
  "published": "2012-06-19T10:39:15.000Z",
  "updated": "2012-06-19T10:39:15.000Z",
  "title": "Generalized Fibonacci and Lucas Numbers of the form $5x^{2}$",
  "authors": [
    "Refik Keskin",
    "Olcay Karaatlı"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $(U_{n}(P,Q) $ and $(V_{n}(P,Q) $ denote the generalized Fibonacci and Lucas sequence, respectively. In this study, we assume that $Q=1.$ We determine all indices $n$ such that $U_{n}=5\\square $ and $U_{n}=5U_{m}\\square $ under some assumptions on $P.$ We show that the equation $V_{n}=5\\square $ has the solution only if $n=1$ for the case when $% P$ is odd. Moreover, we show that the equation $V_{n}=5V_{m}\\square $ has no solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-19T10:39:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11B39",
      "11A07"
    ],
    "keywords": [
      "generalized fibonacci",
      "lucas numbers",
      "lucas sequence",
      "assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.4174K"
    }
  }
}