Monatshefte für Mathematik

, Volume 101, Issue 4, pp 309–315

Dyadic fractions with small partial quotients

  • Harald Niederreiter


It is proved that ifm is a power of 2, then there exists an odd integera with 1≤a<m such that all partial quotients in the continued fraction expansion ofa/m are bounded by 3. The upper bound 3 is best possible. Similar results can be shown for powers of other small numbers.


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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Harald Niederreiter
    • 1
  1. 1.Kommission für MathematikÖsterreichische Akademie der WissenschaftenViennaAustria

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