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Let $k$ and $m$ be two coprime numbers. Let $S_{ij}=\left[ \frac{i+j}{m}\right] -\left[ \frac{i}{m}\right] -% \left[ \frac{j}{m}\right] $, where $\left[ \text{ }\right] $ is the Gauss symbol.( you can see Lemma4 in Tahara). What is the definition of this symbol used here and what is the value of the numbers $S_{k; -k}$ and $S_{k; k}$.

Any help would be appreciated so much. Thank you all.

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?

Let $k$ and $m$ be two coprime numbers. Let $S_{ij}=\left[ \frac{i+j}{m}\right] -\left[ \frac{i}{m}\right] -% \left[ \frac{j}{m}\right] $, where $\left[ \text{ }\right] $ is the Gauss symbol.( you can see Lemma4 in Tahara). What is the definition of this symbol used here and what is the value of the numbers $S_{k; -k)}$ and $S_{k; k}$.

Any help would be appreciated so much. Thank you all.

Let $k$ and $m$ be two coprime numbers. Let $S_{ij}=\left[ \frac{i+j}{m}\right] -\left[ \frac{i}{m}\right] -% \left[ \frac{j}{m}\right] $, where $\left[ \text{ }\right] $ is the Gauss symbol.( you can see Lemma4 in Tahara). What is the definition of this symbol used here and what is the value of the numbers $S_{k; -k}$ and $S_{k; k}$.

Any help would be appreciated so much. Thank you all.

Let $k$ and $m$ be two coprime numbers. Let $S_{ij}=\left[ \frac{i+j}{m}\right] -\left[ \frac{i}{m}\right] -% \left[ \frac{j}{m}\right] $, where $\left[ \text{ }\right] $ is the Gauss symbol.( you can see Lemma4 in Tahara). What is the definition of this symbol used here and what is the value of the number $S_{k(-k)}$.

Any help would be appreciated so much. Thank you all.

Let $k$ and $m$ be two coprime numbers. Let $S_{ij}=\left[ \frac{i+j}{m}\right] -\left[ \frac{i}{m}\right] -% \left[ \frac{j}{m}\right] $, where $\left[ \text{ }\right] $ is the Gauss symbol.( you can see Lemma4 in Tahara). What is the definition of this symbol used here and what is the value of the numbers $S_{k; -k)}$ and $S_{k; k}$.

Any help would be appreciated so much. Thank you all.