New infinite families of congruences modulo 8 for partitions with even parts distinct
Summary: Let \(\mathrm{ped}(n)\) denote the number of partitions of an integer \(n\) wherein even parts are distinct. Recently, \textit{G. E. Andrews} et al. [Ramanujan J. 23, No. 1--3, 169--181 (2010; Zbl 1218.05018)], \textit{S.-C. Chen} [Discrete Math. 311, No. 12, 940--943 (2011; Zbl 1232.11110)], and \textit{S.-P. Cui} and \textit{N. S. S. Gu} [Adv. Appl. Math. 51, No. 4, 507--523 (2013; Zbl 1281.05013)] have derived a number of interesting congruences modulo 2, 3 and 4 for \(\mathrm{ped}(n)\). In this paper we prove several new infinite families of congruences modulo 8 for \(\mathrm{ped}(n)\). For example, we prove that for \(\alpha \geqslant 0\) and \(n\geqslant 0\), \[ \mathrm{ped}\bigg(3^{4\alpha+4}n+\frac{11\times 3^{4\alpha+3}-1}{8}\bigg)\equiv 0 \,(\mathrm{mod}\,8). \]
scientific article; zbMATH DE number 6360683