Abstract
Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $$\mathbb{Q}\left( {\sqrt {{x^2} - 2{y^n}} } \right)$$ whose ideal class group has an element of order n. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
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