{
  "id": "1303.1838",
  "version": "v1",
  "published": "2013-03-07T22:11:04.000Z",
  "updated": "2013-03-07T22:11:04.000Z",
  "title": "The Generalized Fibonacci and Lucas Solutions of The Pell Equations x^2-(a^2b^2-b)y^2=N and x^2-(a^2b^2-2b)y^2=N",
  "authors": [
    "Bilge Peker",
    "Hasan Senay"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this study, we find continued fraction expansion of sqrt(d) when d=a^2b^2-b and d=a^2b^2-2b where a and b are positive integers. We consider the integer solutions of the Pell equations x^2-(a^2b^2-b)y^2=N and x^2-(a^2b^2-2b)y^2=N when N is {+-1,+-4}. We formulate the n-th solution (x_{n},y_{n}) by using the continued fraction expansion. We also formulate the n-th solution (x_{n},y_{n}) in terms of generalized Fibonacci and Lucas sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-07T22:11:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09",
      "11D79",
      "11D45",
      "11A55",
      "11B39",
      "11B50",
      "11B99"
    ],
    "keywords": [
      "pell equations",
      "generalized fibonacci",
      "lucas solutions",
      "continued fraction expansion",
      "n-th solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.1838P"
    }
  }
}