A congruence involving harmonic sums modulo $p^{\alpha }{q}^{\beta }$

Tianxin Cai, Zhongyan Shen, Lirui Jia

In 2014, Wang and Cai established the following harmonic congruence for any odd prime $p$ and positive integer $r$, \begin{equation*} Z(p^{r})\equiv-2p^{r-1}B_{p-3} ~(\bmod ~ p^{r}…