congruence modulo syntax will consist of two individual commands, `\equiv`

and `\mod`

commands.

```
\documentclass{article}
\usepackage{mathtool}
\begin{document}
% Use mathtools for \mod
$$ b \equiv c \mod{m} $$
% \pmod is default command
$$ a \equiv b \pmod{n} $$
$$ a \equiv b \pmod{\frac{m}{(k,m)}} $$
$$ a \equiv b \left(\mod{\frac{m}{(k,m)}}\right) $$
\end{document}
```

**Output : **

But, you notice the output above, where a lot of space has been created by using the `\mod`

and `\pmod`

commands. To solve this problem you need to use `\bmod`

command, or manually solve using `\mathrm`

command.

```
\documentclass{article}
\begin{document}
$$ b \equiv c\;(\bmod{m}) $$
$$ 10+5 \equiv 3\;(\bmod{12}) $$
$$ \frac{p}{q} \equiv f\prod^{n-1}_{i=0}p_i\;(\mathrm{mod}\;m) $$
\end{document}
```

**Output : **

## Some congruence modulo proparties in LaTeX

Best practice is shown by discussing some properties below.

```
\documentclass{article}
\usepackage{mathabx}
\begin{document}
\begin{enumerate}
\item Equivalence: $ a \equiv \modx{0}\Rightarrow a=b $
\item Determination: either $ a\equiv b\; \modx{m} $ or $ a \notequiv b\; \modx{m} $
\item Reflexivity: $ a\equiv a \;\modx{m} $.
\item Symmetry: $ a\equiv b\; \modx{m}\Rightarrow b\equiv a \;\modx{m} $.
\end{enumerate}
\end{document}
```

**Output : **