Tahara refers to the "Gauss symbol" in the article, On the second cohomology groups of semidirect products, Math. Z. 129 (1972) 365--379. For a fixed $n$, let $S_{ij}$ be the expression \begin{equation} \left[ \frac{i+j}{n}\right] -\left[ \frac{i}{n}\right] - \left[ \frac{j}{n}\right] \end{equation} which comes up often in the paper. What does $\left[ \text{ }\right] $ mean here? Also, what then are $S_{k,-k}$ and $S_{k,k}$, assuming $k$ and $n$ are coprime?