Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruences involving $\binom{2k}k^2\binom{3k}km^{-k}$   Let $p>3$ be a prime, and let $m$ be an integer with $p\nmid m$. In the
paper, based on the work of Brillhart and Morton, by using the work of Ishii
and Deuring's theorem for elliptic curves with complex multiplication we solve
some conjectures of Zhi-Wei Sun concerning
$\sum_{k=0}^{p-1}\binom{2k}k^2\binom{3k}km^{-k}\mod {p^2}$.

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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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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: econ