{
  "id": "2103.14487",
  "version": "v1",
  "published": "2021-03-26T14:22:52.000Z",
  "updated": "2021-03-26T14:22:52.000Z",
  "title": "Sums of Fibonacci numbers that are perfect powers",
  "authors": [
    "Volker Ziegler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let us denote by $F_n$ the $n$-th Fibonacci number. In this paper we show that for a fixed integer $y$ there exists at most one integer exponent $a>0$ such that the Diophantine equation $F_n+F_m=y^a$ has a solution $(n,m,a)$ in positive integers satisfying $n>m>0$, unless $y=2,3,4,6$ or $10$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-26T14:22:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect powers",
      "th fibonacci number",
      "integer exponent",
      "diophantine equation",
      "fixed integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}