JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 2, Pages 331 - 347
(August 2005)
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CLASS GROUPS AND QUADRATIC DIOPHANTINE EQUATIONS
R. A. Mollin (Canada)
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Abstract: First, we consider the Diophantine equation of the form x2 ? Dy2 = 16, and provide a criterion for the central norm in the simple continued fraction expansion of
to be 16 in association with norm 32. This involves congruence conditions on the fundamental unit of the underlying real quadratic order. Then we provide necessary and sufficient conditions for the class group of complex quadratic fields to have a cyclic subgroup of order n > 1, with generator of a certain form. |
Keywords and phrases: quadratic Diophantine equations, continued fractions, central norms, class group, generator. |
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