Gireesh and Mahadeva Naika [‘On 3-regular partitions in 3-colors’, Indian J. Pure Appl. Math.50 (2019), 137–148] proved an infinite family of congruences modulo powers of 3 for the function $p_{\{3,3\}}(n)$ , the number of 3-regular partitions in three colours. In this paper, using elementary generating function manipulations and classical techniques, we significantly extend the list of proven arithmetic properties satisfied by $p_{\{3,3\}}(n).$

中文翻译：

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三色三正则分区的算术性质

Gireesh 和 Mahadeva Naika ['On 3-regular partitions in 3-colors',印度 J. Pure Appl。数学。50(2019), 137–148] 证明了函数的无限同余族 3 的模幂$p_{\{3,3\}}(n)$，三种颜色的 3 规则分区的数量。在本文中，使用初等生成函数操作和经典技术，我们显着扩展了经过验证的算术属性列表，满足$p_{\{3,3\}}(n).$