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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 and products of continued fractions


Author: T. W. Cusick
Journal: Proc. Amer. Math. Soc. 27 (1971), 35-38
MSC: Primary 10.31
MathSciNet review: 0269603
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Abstract: It is proved that every real number is representable as a sum of two real numbers each of which has a fractional part whose continued fraction expansion contains no partial quotient less than 2, and that every real number not less than one is representable as a product of two real numbers with the same property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0269603-3
PII: S 0002-9939(1971)0269603-3
Keywords: Continued fractions, Cantor sets, sums of sets
Article copyright: © Copyright 1971 American Mathematical Society