Let s(n) be the number of 1-shell totally symmetric plane partitions (TSPPs) of n. In this paper, an infinite family of congruences modulo powers of 5 for s(n) will be deduced through an elementary approach. Namely,

$$\begin{aligned} s\left( 2\cdot 5^{2\alpha -1}n+5^{2\alpha -1}\right) \equiv 0 \pmod {5^{\alpha }}. \end{aligned}$$

中文翻译：

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1-Shell完全对称平面分区（TSPP）的5模功率

令小号（Ñ）是1 -壳完全对称面的分区（TSPPs）的数量Ñ。在本文中，将通过基本方法推导s（n）的5模幂的无穷大同余模。即

$$ \ begin {aligned} s \ left（2 \ cdot 5 ^ {2 \ alpha -1} n + 5 ^ {2 \ alpha -1} \ right）\ equiv 0 \ pmod {5 ^ {\ alpha}} 。\ end {aligned} $$