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Continued Fractions, Jacobi Symbols, and Quadratic Diophantine Equations

Published online by Cambridge University Press:  20 November 2018

R. A. Mollin  and
A. J. van der Poorten
R. A. Mollin
Affiliation:
Mathematics Department University of Calgary Calgary, Alberta T2N 1N4, website: http://www.math.ucalgary.ca/∼ramollin/ e-mail: [email protected]
A. J. van der Poorten
Affiliation:
School of MPCE Macquarie University Sydney Sydney, N.S.W. 2109 Australia, website: http://www.mpce.mq.edu.au/alf e-mail: [email protected]
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Abstract

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The results herein continue observations on norm form equations and continued fractions begun and continued in the works [1]−[3], and [5]−[6].

Keywords

11R1111D0911R2911R65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 2 , 01 June 2000 , pp. 218 - 225
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Chowla, P. and Chowla, S., Problems on periodic simple continued fractions. Proc. Nat. Acad. Sci. U.S.A. 69(1972), 37–45.Google Scholar
[2] Friesen, C., Legendre symbols and continued fractions. Acta Arith. LIX(1991), 365–379.Google Scholar
[3] Mollin, R. A., Jacobi symbols, ambiguous ideals, and continued fractions. Acta Arith. (4) LXXXV(1998), 331– 349.Google Scholar
[4] Mollin, R. A., Quadratics. CRC Press, Boca Raton-New York-London, 1996.Google Scholar
[5] Mollin, R. A., van der Poorten, A. J., and Williams, H. C., Halfway to a solution of x2 − Dy2 = −3. Th, J.éorie Nombres, Bordeaux 6(1994), 421–459.Google Scholar
[6] Schinzel, A., On two conjectures of P. Chowla and S. Chowla concerning continued fractions, Ann. Mat. Appl. 98(1974), 111–117.Google Scholar