# How do you write congruence modulo(mod n) in LaTeX?

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 :

One request!

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