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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

1. Elte, E. L., Aanvulling eener eigenschap der periodieke kettingbreuken, Nieuw Archief voor Wiskunde (2) 15 (1925), 55-59.Google Scholar
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