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Let $a(m,n)$ be the number of partitions with no more than $m$ parts, each part (strictly) less than $n$, and the sum a multiple of $n$. Then $a(m,n)=a(n,m)$.
Let $a(m,n)$ be the number of partitions with no more than $m$ parts, each part less than $n$, and the sum a multiple of $n$. Then $a(m,n)=a(n,m)$.
Let $a(m,n)$ be the number of partitions with no more than $m$ parts, each part (strictly) less than $n$, and the sum a multiple of $n$. Then $a(m,n)=a(n,m)$.
