Byungchan Kim Seoul National University of Science and Technology
Abstract : In this note, we investigate partition congruences for a certain type of partition function, which is named as the overcubic partition pairs in light of the literature. Let $\overline{cp}(n)$ be the number of overcubic partition pairs. Then we will prove the following congruences: \begin{align*} \overline{cp}(8n+7) \equiv 0 \pmod{64} \quad\mbox{and}\quad \overline{cp}(9m+3) \equiv 0 \pmod{3}. \end{align*}
