Monatshefte für Mathematik

, Volume 101, Issue 4, pp 309-315

First online:

Dyadic fractions with small partial quotients

  • Harald NiederreiterAffiliated withKommission für Mathematik, Österreichische Akademie der Wissenschaften

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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.