Congruences modulo powers of 5 for k-colored partitions

Let p−k(n) enumerate the number of k-colored partitions of n. In this paper, we establish some infinite families of congruences modulo 25 for k-colored partitions. Furthermore, we prove some infinite families of Ramanujan-type congruences modulo powers of 5 for p−k(n) with k=2,6, and 7. For example, for all integers n≥0 and α≥1, we prove thatp−2(52α−1n+7×52α−1+112)≡0(mod5α) andp−2(52αn+11×52α+112)≡0(mod5α+1).