Congruences modulo p2p2 and p3p3 for k dots bracelet partitions with k=mpsk=mps

We find several new congruences modulo 2 for 11 dots bracelet partitions and congruences modulo p2p2 and p3p3 for k   dots bracelet partitions for any prime p>3p>3 and k=mpsk=mps with s≥2s≥2 and s≥3s≥3, respectively. We also find a relation between 5-core partitions and Ramanujan's famous tau function τ(n)τ(n) and several new congruences modulo 9 and 25 for 3- and 5-core partitions, respectively.