Symmetry and Prime Divisibility Properties of Partitions of $n$ into Exactly $m$ Parts

Let p(n,m) denote the number of partitions of n into exactly m parts. In this paper we uncover new congruences for the function p(n,m) and give an alternate proof to a known theorem in addition to extending it. The methods of proof rely on identifying generating functions to polynomials and then using the symmetric properties of those polynomials. The theorems proved here provide further motivation and description for a full characterisation of Ramanujan-like divisibility statements about the partition numbers p(n,m).