Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruences modulo powers of 3 for 2-color partition triples   Let $p_{k,3}(n)$ enumerate the number of 2-color partition triples of $n$
where one of the colors appears only in parts that are multiples of $k$. In
this paper, we prove several infinite families of congruences modulo powers of
3 for $p_{k,3}(n)$ with $k=1, 3$, and $9$. For example, for all integers
$n\geq0$ and $\alpha\geq1$, we prove that \begin{align*}
p_{3,3}\left(3^{\alpha}n+\dfrac{3^{\alpha}+1}{2}\right)
&\equiv0\pmod{3^{\alpha+1}} \end{align*} and \begin{align*}
p_{3,3}\left(3^{\alpha+1}n+\dfrac{5\times3^{\alpha}+1}{2}\right)
&\equiv0\pmod{3^{\alpha+4}}. \end{align*}

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat