New infinite families of congruences for 5-core and 7-core partitions

Abstract

Let \(a_t(n)\) denote the number of t-core partitions of n. In recent years, a number of congruences for \(a_t(n)\) have been discovered for some small t. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\). Motivated by their work, we prove some new infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\) by utilizing Newman's identities.