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On the Continued Fractions of Conjugate Quadratic Irrationalities

Published online by Cambridge University Press:  20 November 2018

Fritz Herzog
Fritz Herzog*
Affiliation:
Department of Mathematics Michigan State University East LansingMichigan48824
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Let

1

be the simple continued fraction (SCF) of an irrational number x. The partial quotients ai which we shall sometimes refer to as the "terms" of the SCF are integers and, for i ≥ 2, they are positive. If x is a quadratic irrationality then, by Lagrange's Theorem, the right side of (1) becomes periodic from some point on.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 199 - 206
Copyright
Copyright © Canadian Mathematical Society 1980

References

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2. Kraitchik, M., Théorie des Nombres, vol. II, Paris (1926).Google Scholar
3. Perron, O., Die Lehre von den Kettenbrüchen, 3rd edition, vol. I, Stuttgart (1954).Google Scholar
4. Serret, J.-A., Cours d' Algèbre Supérieure, 7thv edition, vol. I, Paris (1928).Google Scholar