2 problems

Let $NT(r,m,n)$ denote the total number of parts in partitions of $n$ whose rank is congruent to $r$ modulo $m$, and let $M_{\omega}(r,m,n)$ denote the total number of ones in part…

For $n\geq 1$, let $M(\leq m,n)$ denote the number of partitions of $n$ with crank less than or equal to $m$, and let $N(\leq m,n)$ denote the number of partitions of $n$ with rank…