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Journal of the Ramanujan Mathematical Society

Volume 39, Issue 2, June 2024  pp. 171–185.

Congruence properties modulo powers of 2 for two partition functions

Authors:  Dazhao Tang
Author institution:School of Mathematical Sciences, Chongqing Normal University, Chongqing~401331, P.R.~China.

Summary:  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).


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