New congruences modulo 5 for the number of 2-color partitions

Abstract

Let pk(n) be the number of 2-color partitions of n where one of the colors appears only in parts that are multiples of k. In this paper, we find some interesting congruences modulo 5 for pk(n) for k∈{2,3,4} by employing Ramanujan's theta function identities and some identities for the Rogers–Ramanujan continued fraction. The congruence for p2(n) was earlier proved by Chen and Lin with the aid of modular forms.