Cristina Ballantine
College of the Holy Cross, Worcester, USA

A partition of a nonnegative integer $n$ is a way to write $n$ as an unordered sum of positive integers. Denote by $p(n)$ be the number of partitions of $n$. Asymptotically, how often is $p(n)$ even? We do not know, but it is conjectured that $p(n)$ is even half the time. We will consider the number, $b_3(n)$, of $3$-regular partitions, i.e., partitions with no parts divisible by $3$, and find infinitely many arithmetic progressions where $b_3(n)$ takes even values. To prove our result we investigate a quadratic form in a classical way. This is joint work with Mircea Merca and Cristian-Silviu Radu.