{
  "id": "1409.3790",
  "version": "v1",
  "published": "2014-09-12T17:00:13.000Z",
  "updated": "2014-09-12T17:00:13.000Z",
  "title": "Rationality and power",
  "authors": [
    "Sam Chow",
    "Bin Wei"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We produce an infinite family of transcendental numbers which, when raised to their own power, become rational. We extend the method, to investigate positive rational solutions to the equation $x^x = \\alpha$, where $\\alpha$ is a fixed algebraic number. We then explore the consequences of $x^{P(x)}$ being rational, if $x$ is rational and $P(x)$ is a fixed integer polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-12T17:00:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A99",
      "11D61",
      "11J72",
      "11J81"
    ],
    "keywords": [
      "rationality",
      "positive rational solutions",
      "transcendental numbers",
      "fixed algebraic number",
      "fixed integer polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.3790C"
    }
  }
}