New Infinite Families of Congruences Modulo 8 for Partitions with Even Parts Distinct

Ernest X. W. Xia

Abstract


Let $ped(n)$ denote the number of partitions of an integer $n$ wherein even parts are distinct. Recently, Andrews, Hirschhorn and Sellers, Chen, and Cui and Gu have derived a number of interesting congruences modulo 2, 3 and 4 for $ped(n)$. In this paper we prove several new infinite families of congruences modulo 8 for $ped(n)$. For example, we prove that for $ \alpha \geq 0$ and $n\geq 0$,
\[
 ped\left(3^{4\alpha+4}n+\frac{11\times 3^{4\alpha+3}-1}{8}\right)\equiv 0 \  ({\rm mod \ 8}).
\]

Keywords


partition; congruence; regular partition

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