{
  "id": "2202.13182",
  "version": "v1",
  "published": "2022-02-26T16:53:54.000Z",
  "updated": "2022-02-26T16:53:54.000Z",
  "title": "On solutions of the Diophantine equation $L_n+L_m=3^a$",
  "authors": [
    "Pagdame Tiebekabe",
    "Ismaila Diouf"
  ],
  "journal": "Malaya Journal of Matematik, 2021, Volume 9",
  "doi": "10.26637/mjm904/007",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $(L_n)_{n\\geq 0}$ be the Lucas sequence given by $L_0 = 2, L_1 = 1$ and $L_{n+2} = L_{n+1}+L_n$ for $n \\geq 0$. In this paper, we are interested in finding all powers of three which are sums of two Lucas numbers, i.e., we study the exponential Diophantine equation $L_n + L_m = 3^{a}$ in nonnegative integers $n, m,$ and $a$. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-26T16:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11J86"
    ],
    "keywords": [
      "baker-davenport reduction method",
      "exponential diophantine equation",
      "diophantine approximation",
      "main theorem",
      "lucas numbers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}