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Proceedings of the American Mathematical Society

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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)$.

References [Enhancements On Off] (What's this?)

  • [1] T. W. Cusick, Sums and products of continued fractions, Proc. Amer. Math. Soc. 27 (1971), 35-38. MR 0269603 (42:4498)
  • [2] Marshall Hall, Jr., On the sum and product of continued fractions, Ann. of Math. (2) 48 (1947), 966-993. MR 9, 226. MR 0022568 (9:226b)

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Keywords: Continued fractions, Cantor sets, sums of sets
Article copyright: © Copyright 1971 American Mathematical Society

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