Sums and products of continued fractions

T. W. Cusick

doi:10.1090/S0002-9939-1971-0269603-3

Sums and products of continued fractions

T. W. Cusick

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English
Pages (from-to)	35-38
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	27
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1971-0269603-3
State	Published - Jan 1971

Keywords

Cantor sets
Continued fractions
Sums of sets

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10.1090/S0002-9939-1971-0269603-3

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title = "Sums and products of continued fractions",

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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AB - 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.

KW - Cantor sets

KW - Continued fractions

KW - Sums of sets

UR - https://www.scopus.com/pages/publications/0039454080

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DO - 10.1090/S0002-9939-1971-0269603-3

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AN - SCOPUS:0039454080

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VL - 27

SP - 35

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

Sums and products of continued fractions

Abstract

Keywords

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