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A Characterization of the Quadratic Irrationals

Published online by Cambridge University Press:  20 November 2018

Tom C. Brown
Tom C. Brown*
Affiliation:
Department of Mathematics and Statistics Simon Fraser University Burnaby, BC V5A ISA
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Abstract

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Let α be a positive irrational real number, and let fα (n) = [(n + l)α] — [nα] — [α],n > 1, where [x] denotes the greatest integer not exceeding x. It is shown that the sequence fα has a certain 'substitution property' if and only if α is the root of a quadratic equation over the rationals.

Keywords

10L10

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 36 - 41
Copyright
Copyright © Canadian Mathematical Society 1991

References

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