How to write the congruence modulo n symbol?

Question

When a is the remainder when b is divided by n, we say b is congruent to a mod n.

How is it typeset using LaTeX?

You also have b\equiv a \mod{n} (no parentheses, same spacing) or b\equiv a \bmod{n} (no parentheses, smaller spacing). All this is explained in the amsmath documentation. — Bernard, Sep 23 '21 at 18:29
Related: Writing mod in congruence problems without leading space — Werner, Oct 02 '21 at 05:34
There are many notations for congruence of integers modulo an integer, and there are good reasons for using different ones in different situations. See https://github.com/Ben-McKay/concrete-algebra — Benjamin McKay, Oct 02 '21 at 07:32

score 4 · Answer 1 · answered Oct 02 '21 at 09:27

There are several ways, choose the one you prefer.

\documentclass{article}
\usepackage{amsmath}
\renewcommand{\arraystretch}{1.5} % just to make the lines spread out
\begin{document}
\begin{tabular}{lll}
\verb|$a\equiv b \pmod{n}$| & $a\equiv b \pmod{n}$ \
\verb|$a\equiv b \mod{n}$|  & $a\equiv b \mod{n}$ \
\verb|$a\equiv b \pod{n}$|  & $a\equiv b \pod{n}$ \
\verb|$a\equiv b \bmod{n}$| & $a\equiv b \bmod{n}$ & (wrong)
\end{tabular}
\end{document}

Don't forget the braces: try a\equiv b \pmod 11 or a\equiv b \pmod pq and see why.

The last one is marked “wrong”, because the usage is improper: \bmod should be used for the “modulo” binary operation (the one that is often denoted by % in computing).

score 1 · Accepted Answer · answered Sep 23 '21 at 16:28

1

Use pmod n. It is known to work.

answered Sep 23 '21 at 16:28

F. A. Mala

229

It would be clearer if you wrote out a more complete example, like $n \equiv 1 \pmod{k}$. – Benjamin McKay Oct 02 '21 at 07:33

How to write the congruence modulo n symbol?

2 Answers2