Abstract
We show how the solution to certain diophantine equations involving the discriminant of complex quadratic fields leads to the divisibility of the class numbers of the underlying fields. This not only generalizes certain results in the literature such as [2], [4]–[6] but also shows why certain hypotheses made in these results are actually unnecessary since, as our criteria demonstrate, these hypotheses are forced by the solution of the diophantine equations involved. Our methods are based only on the most elementary properties of a principal ideal in a complex quadratic field.
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