Congruences for partitions with odd parts distinct modulo 5

Abstract

Hirschhorn and Sellers studied arithmetic properties of the number of partitions with odd parts distinct modulo powers of 3. In this paper, we focus on congruences for pod (n) modulo 5. For example, for α ≥ 2 and n ≥ 0, we have [Formula: see text] In addition, applying some equations given by Hirschhorn and Sellers [Arithmetic properties of partitions with odd parts distinct, Ramanujan J.22 (2010) 273–284], some new congruences are established.