On the divisibility of 7-elongated plane partition diamonds by powers of 8.

In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the k -elongated plane partition function d k (n) by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function d 7 (n). We prove that such a congruence family exists — indeed, for powers of 8. The proof utilizes only classical methods, i.e. integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for d k (n) which require more modern methods to prove. [ABSTRACT FROM AUTHOR]