{
  "id": "1610.02774",
  "version": "v1",
  "published": "2016-10-10T05:31:54.000Z",
  "updated": "2016-10-10T05:31:54.000Z",
  "title": "Prime powers in sums of terms of binary recurrence sequences",
  "authors": [
    "Eshita Mazumdar",
    "S. S. Rout"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\{u_{n}\\}_{n \\geq 0}$ be a non-degenerate binary recurrence sequence with positive, square-free discriminant and $p$ be a fixed prime number. In this paper, we have shown the finiteness result for the solutions of the Diophantine equation $u_{n_{1}} + u_{n_{2}} + \\cdots + u_{n_{t}} = p^{z}$ with some conditions on $n_i $ for $1\\leq i \\leq t$. Moreover, we explicitly find all the powers of three which are sums of three balancing numbers using the lower bounds for linear forms in logarithms. Further, we use a variant of Baker-Davenport reduction method in Diophantine approximation due to Dujella and Peth\\H{o}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-10T05:31:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11D45",
      "11J86"
    ],
    "keywords": [
      "prime powers",
      "non-degenerate binary recurrence sequence",
      "baker-davenport reduction method",
      "diophantine approximation",
      "square-free discriminant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}