Congruences for the number of partitions and bipartitions with distinct even parts

Abstract

Let ped(n) denote the number of partitions of n wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for ped(n) modulo 8. We also examine the behavior of ped−2(n) modulo 8 in detail where ped−2(n) denotes the number of bipartitions of n with even parts distinct. As a result, we find infinite families of congruences for ped−2(n) modulo 8.