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Estimating |α – p / q|

Published online by Cambridge University Press:  09 April 2009

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

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An estimate for q2|α – p/;q| is obtained by considering the relation between the continued fractions for α and p / q. This leads to an extension of the standard result “q2|α – p/q| < 1 imples that for some n, p/q = (ipn + pn-1) / (iqn + qn-1) where i = 0, 1 or an+1 −1”.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 202 - 206
Copyright
Copyright © Australian Mathematical Society 1982

References

Lang, S. (1966), Introduction to diophantine approximation (Addison Wesley).Google Scholar
Niven, I. and Zuckerman, H. S. (1972), An introduction to the theory of numbers (third edition, John Wiley and Sons Inc.).Google Scholar
Worley, R. T. (1973), ‘Sequences of continued fractions’, J. Austral. Math. Soc. 15, 112116.–Google Scholar
Worley, R.T. (1977), ‘Restricted diophantine approximation’, J. Austral. Math. Soc. Ser. A. 24, 425–439.CrossRefGoogle Scholar