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International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 9, Pages 565-571

Continued fractions and class number two

Mathematics Department, University of Calgary, Calgary, AB T2N 1N4, Canada

Received 12 September 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well-known result by Hendy (1974) for complex quadratic fields. We illustrate with several examples.