  Let $p$ be a prime and ${\mathcal{P}_{p}}$ the set of positive integers which
are prime to $p$. We establish the following interesting congruence
\[\sum\limits_{\begin{smallmatrix}
  i+j+k={{p}^{r}}
  i,j,k\in {\mathcal{P}_{p}} \end{smallmatrix}}{\frac{{{(-1)}^{i}}}{ijk}}\equiv
\frac{{{p}^{r-1}}}{2}{{B}_{p-3}}\, (\bmod \, {{p}^{r}}).\]
