Ramanujan-type congruences modulo 8 for 7- and 23-core partition functions

Abstract

Recently, Radu and Sellers proved numerous congruences modulo powers of 2 for \( (2k+1)\)-core partition functions by employing the theory of modular forms. In this paper, employing Ramanujan’s theta function identities, we prove many infinite families of congruences modulo 8 for 7-core partition function. Our results generalize the congruences modulo 8 for 7-core partition function discovered by Radu and Sellers. Furthermore, we present new proofs of congruences modulo 8 for 23-core partition function. These congruences were first proved by Radu and Sellers.