Two infinite families of congruences modulo 9 for overcubic partition pairs
Volume 147 / 2017
Colloquium Mathematicum 147 (2017), 115-123
MSC: Primary 05A17; Secondary 11P83.
DOI: 10.4064/cm6843-4-2016
Published online: 9 December 2016
Abstract
Let $\overline {b}(n)$ denote the number of overcubic partition pairs of $n$. Applying the theory of modular forms, Kim obtained two congruences for $\overline {b}(n)$ modulo $3$ and $64$. More congruences modulo $3$ and $5$ have been found by the first author of the present paper. In this paper, we proceed with the study of the congruence properties of $\overline {b}(n)$ and establish two infinite families of congruences modulo $9$.
