Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponents of class groups of certain imaginary quadratic fields   Let $n>1$ be an odd integer. We prove that there are infinitely many
imaginary quadratic fields of the form $\mathbb{Q}(\sqrt{x^2-2y^n})$ whose
ideal class group has an element of order $n$. This family gives a counter
example to a conjecture by H. Wada \cite{WA70} on the structure of ideal class
groups.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom