Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of cyclic subgroups of finite abelian groups and Menon's
  identity   In this note, we give a new formula for the number of cyclic subgroups of a
finite abelian group. This is based on applying the Burnside's lemma to a
certain group action. Also, it generalizes the well-known Menon's identity.

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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: q-fin