Arithmetic Properties of Partitions with 1-colored Even Parts and r-colored Odd Parts
Abstract
Recently, Hirschhorn and Sellers defined the partition function ar(n), which counts the number of partitions of n wherein even parts come in only one color, while the odd parts may appear in one of r-colors for fixed r1. The aim of this paper is to prove several new infinite families of congruences modulo 3 and 5 by employing a result of Newman and theory of modular forms.
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