Congruences modulo 4 for the number of 3-regular partitions

Abstract

The last decade has seen an abundance of congruences for b ℓ (n), the number of ℓ-regular partitions of n. Notably absent are congruences modulo 4 for b 3 (n). In this paper, we introduce Ramanujan type congruences modulo 4 for b 3 (2n) involving some primes p congruent to 11,13,17,19,23 modulo 24.