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Euclid's Algorithm in real Quadratic Fields

Published online by Cambridge University Press:  20 November 2018

H. Chatland  and
H. Davenport
H. Chatland
Affiliation:
The Ohio State Universityand , University College, London
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1. Let m be a positive square-free integer. Euclid's Algorithm is said to hold in the field if, given any non-integral element a in the field, an integer a can be found so that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 289 - 296
Copyright
Copyright © Canadian Mathematical Society 1950

References

[1] Davenport, H., Indefinite binary quadratic forms, and Euclid's Algorithm in real quadratic fields, Proc. London Math. Soc. (in course of publication).Google Scholar
[2] Chatland, H., On the Euclidean Algorithm in quadratic number fields, Bull. Amer. Math. Soc., vol. 55 (1949), 948–953.Google Scholar
[3] Erdös, P. and Ko, Chao, Note on the Euclidean Algorithm, J. London Math. Soc., vol. 13(1938), 3–8.Google Scholar
[4] K.|Inkeri, Über den Euklidischen Algorithmus in quadratischen Zahlkörpern, Annales Academiae Scientiarum Fennicae, vol. 41 (1947), 5–34.Google Scholar