Congruence properties modulo powers of 2 for two partition functions

Let Q ( n ) denote the number of partitions of n into distinct parts. Several scholars successively studied congruence properties modulo powers of 5 and arithmetic properties modulo powers of 2 satisfied by Q ( n ). Let f ( n ) denote the number of 1 -shell totally symmetric plane partitions of n . Congruence properties modulo powers of 2 and 5 for f ( n ) were subsequently considered by some scholars. In this paper, we prove a number of internal congruences and congruences modulo powers of 2 enjoyed by Q ( n ) and f ( n ). Moreover, we pose two conjectures on internal congruence families and congruence families modulo any powers of 2 enjoyed by Q ( n ) and f ( n ).