Proofs of two conjectures on congruences of overcubic partition triples

Abstract

Let $\overline{bt}(n)$ denote the number of overcubic partition triples of $n$. Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for $\overline{bt}(n)$. Recently, Saikia and Sarma established some congruences modulo 64 for $\overline{bt}(n)$ by using both elementary techniques and the theory of modular forms. In their paper, they also posed two conjectures on infinite families of congruences modulo 64 and 128 for $\overline{bt}(n)$. In this paper, we confirm the two conjectures.