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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Sums of sets of continued fractions


Authors: T. W. Cusick and R. A. Lee
Journal: Proc. Amer. Math. Soc. 30 (1971), 241-246
MSC: Primary 10.31
MathSciNet review: 0282924
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Abstract: For each integer $ k \geqq 2$, let $ S(k)$ denote the set of real numbers $ \alpha $ such that $ 0 \leqq \alpha \leqq {k^{ - 1}}$ and $ \alpha $ has a continued fraction containing no partial quotient less than k. It is proved that every number in the interval [0, 1] is representable as a sum of k elements of $ S(k)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0282924-3
PII: S 0002-9939(1971)0282924-3
Keywords: Continued fractions, Cantor sets, sums of sets
Article copyright: © Copyright 1971 American Mathematical Society