Abstract
Using the Markoff theorem on indefinite binary quadratic forms it is shown that every element of the class group of any real quadratic order of discriminant d has an ideal of norm less than or equal to 1+⌊d3⌋. This bound is best possible as there are quadratic orders of discriminant d which have ideal classes where the least norm is 1+⌊d3⌋. These discriminants are explicitly given and their connection to the Markoff conjecture is highlighted.
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