Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic Properties of Partition Triples With Odd Parts Distinct   Let $\mathrm{pod}_{-3}(n)$ denote the number of partition triples of $n$
where the odd parts in each partition are distinct. We find many arithmetic
properties of $\mathrm{pod}_{-3}(n)$ involving the following infinite family of
congruences: for any integers $\alpha \ge 1$ and $n\ge 0$,
\[\mathrm{pod}_{-3}\Big({{3}^{2\alpha +2}}n+\frac{23\times {{3}^{2\alpha
+1}}+3}{8}\Big)\equiv 0 \pmod{9}.\] We also establish some arithmetic relations
between $\mathrm{pod}(n)$ and $\mathrm{pod}_{-3}(n)$, as well as some
congruences for $\mathrm{pod}_{-3}(n)$ modulo 7 and 11.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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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: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th