Monatshefte für Mathematik

, Volume 101, Issue 4, pp 309–315

Dyadic fractions with small partial quotients

  • Harald Niederreiter

DOI: 10.1007/BF01559394

Cite this article as:
Niederreiter, H. Monatshefte für Mathematik (1986) 101: 309. doi:10.1007/BF01559394


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.

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

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