{
  "id": "2206.14067",
  "version": "v1",
  "published": "2022-06-28T15:09:45.000Z",
  "updated": "2022-06-28T15:09:45.000Z",
  "title": "Number of solutions to $a^x + b^y = c^z$, A Shorter Version",
  "authors": [
    "Reese Scott",
    "Robert Styer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at most two solutions in positive integers $(x,y,z)$ to the equation $a^x + b^y = c^z$. There are an infinite number of $(a,b,c)$ giving exactly two solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-28T15:09:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61"
    ],
    "keywords": [
      "shorter version",
      "relatively prime integers",
      "odd integer",
      "infinite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}