{
  "id": "1706.10294",
  "version": "v1",
  "published": "2017-06-30T17:52:55.000Z",
  "updated": "2017-06-30T17:52:55.000Z",
  "title": "On perfect powers that are sums of two Fibonacci numbers",
  "authors": [
    "Florian Luca",
    "Vandita Patel"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the equation $F_n + F_m = y^p$, where $F_n$ and $F_m$ are respectively the $n$-th and $m$-th Fibonacci numbers and $p \\ge 2$. We find all solutions under the assumption $n \\equiv m \\pmod{2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-30T17:52:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect powers",
      "th fibonacci numbers",
      "assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}