{
  "id": "math/0611622",
  "version": "v1",
  "published": "2006-11-20T22:58:02.000Z",
  "updated": "2006-11-20T22:58:02.000Z",
  "title": "About the fractional parts of the powers of the rational numbers",
  "authors": [
    "Bakir Farhi"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p/q$ ($p, q \\in \\mathbb{N}^*$) be a positive rational number such that $p > q^2$. We show that for any $\\epsilon > 0$, there exists a set $A(\\epsilon) \\subset [0, 1[$, with finite border and with Lebesgue measure $< \\epsilon$, for which the set of positive real numbers $\\lambda$ satisfying $<\\lambda (p / q)^n> \\in A(\\epsilon)$ $(\\forall n \\in \\mathbb{N})$ is uncountable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-20T22:58:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K06"
    ],
    "keywords": [
      "fractional parts",
      "positive real numbers",
      "positive rational number",
      "finite border"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11622F"
    }
  }
}