Arithmetic properties of 3-regular bi-partitions with designated summands

M. S. Mahadeva Naika and S. Shivaprasada Nayaka

Abstract: Recently Andrews, Lewis and Lovejoy introduced the partition functions $PD\left(n\right)$ defined by the number of partitions of $n$ with designated summands and they found several modulo 3 and 4. In this paper, we find several congruences modulo 3 and 4 for $PB{D}_3\left(n\right)$, which represent the number of 3-regular bi-partitions of $n$ with designated summands. For example, for each    $n\ge 1$ and $\alpha \ge 0$    $PB{D}_3(4·3^{\alpha +2}n+10·3^{\alpha +1})\equiv 0(mod3)$.

Keywords: Partitions; designated summands; congruences.

Classification (MSC2000): 05A17; 11P83

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