New congruences for 2-color partitions

Let pk(n)pk(n) denote the number of 2-color partitions of n where one of the colors appears only in parts that are multiples of k  . We will prove a conjecture of Ahmed, Baruah, and Dastidar on congruences modulo 5 for pk(n)pk(n). Moreover, we will present some new congruences modulo 7 for p4(n)p4(n).