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Denominator sequences for continued fractions, III

Published online by Cambridge University Press:  09 April 2009

R. T. Worley
R. T. Worley
Affiliation:
Department of Mathematics Monash UniversityClayton, Victoria 3168Australia
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Abstract

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It is shown that for every irrational α the set of α′ for which α and α′ have infinitely many convergents with the same denomintor, has the cardinality of the continuum.

Subject classification (Amer. Math. Soc. (MOS), 1970): 10 A 30.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 53 - 56
Copyright
Copyright © Australian Mathematical Society 1978

References

Schmidt, W. M. (1967), “On simultaneous approximations of two algebraic numbers by rationals”, Acta Math. 119, 27–50.Google Scholar
Worley, R. T. (1973), “Denominator sequences of continued fractions.’, J. Austral. Math. Soc. 15, 112–116.Google Scholar