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Dyadic fractions with small partial quotients

Abstract

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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Niederreiter, H. Dyadic fractions with small partial quotients. Monatshefte für Mathematik 101, 309–315 (1986). https://doi.org/10.1007/BF01559394

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  • DOI: https://doi.org/10.1007/BF01559394

Keywords

  • Continue Fraction Expansion
  • Partial Quotient
  • Dyadic Fraction