The pa-Regular Partition Function Modulo pj Original Research Article

Let bℓ(n) denote the number of ℓ-regular partitions of n, where ℓ is a positive power of a prime p. We study in this paper the behavior of bℓ(n) modulo powers of p. In particular, we prove that for every positive integer j, bℓ(n) lies in each residue class modulo pj for infinitely many values of n.