How to Write Mod in LaTeX

Use \bmod between two numbers: a \bmod b. After a congruence use \pmod{n}, which adds space and parentheses: a \equiv b \pmod{n}. Never type the letters m-o-d directly in math; they come out as an italic product.

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The four mod commands

a \bmod b
$a mod b$
Binary operator: "a mod b" with operator spacing.
a \equiv b \pmod{n}
$a \equiv b (\mod n)$
Parenthesised: "(mod n)" with extra space before it.
a \equiv b \mod{n}
$a \equiv b \mod n$
amsmath: "mod n" without parentheses.
a \equiv b \pod{n}
$a \equiv b (n)$
amsmath: "(n)", parentheses without the word.
\operatorname{mod}
$\mod$
Upright "mod" with operator spacing you control.

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Modulo (mod) examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Remainder
$17 mod 5 = 2$
LaTeX
```
17 \bmod 5 = 2
```
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Congruence
$17 \equiv 2 (\mod 5)$
LaTeX
```
17 \equiv 2 \pmod{5}
```
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Euler's theorem
$a^{φ (n)} \equiv 1 (\mod n)$
LaTeX
```
a^{\varphi(n)} \equiv 1 \pmod{n}
```
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Hash function
$h (k) = k mod m$
LaTeX
```
h(k) = k \bmod m
```
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Chinese remainder theorem
$\begin{aligned} x & \equiv 2 (\mod 3) \\ x & \equiv 3 (\mod 5) \end{aligned}$
LaTeX
```
\begin{aligned} x &\equiv 2 \pmod{3} \\ x &\equiv 3 \pmod{5} \end{aligned}
```
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Inline-friendly form
$a \equiv b (\mod n)$
LaTeX
```
a \equiv b \;(\operatorname{mod} n)
```
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Which one to use

\bmod is for the operation that returns a remainder, as in programming. \pmod is for the relation "congruent modulo n" and is what most number theory texts use. \mod and \pod come from amsmath for authors who prefer "mod n" without parentheses or parentheses without "mod".

Too much space before (mod n)?

\pmod adds a quad of space in display math and less inline. If it looks too wide in running text, write \;(\operatorname{mod} n) yourself, as in the last example.

Common mistakes

Typed letters become italic variables m·o·d.
Instead of
```
a \equiv b (mod n)
```
Write
```
a \equiv b \pmod{n}
```
\pmod puts parentheses around b; for "a mod b" use \bmod.
Instead of
```
a \pmod b
```
Write
```
a \bmod b
```
% starts a comment in LaTeX; the rest of the line disappears.
Instead of
```
a % b
```
Write
```
a \bmod b
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\bmod and \pmod work without packages; \mod and \pod need amsmath.
MathJax and KaTeX
MathJax and KaTeX support \bmod, \pmod, \mod and \pod.
Microsoft Word
In a Word equation type "mod" and Word sets it upright as a function name, or use \pmod-style text: (mod n).

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Modulo (mod) in LaTeX: questions

How do I write mod in LaTeX?: a \bmod b for the operation, a \equiv b \pmod{n} for a congruence.
What is the difference between \bmod and \pmod?: \bmod is a binary operator; \pmod{n} writes "(mod n)" after a congruence.
Why is my mod italic?: You typed the letters. Use one of the mod commands or \operatorname{mod}.

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How to Write Mod in LaTeX

The four mod commands

Try it live

Modulo (mod) examples

Remainder

Congruence

Euler's theorem

Hash function

Chinese remainder theorem

Inline-friendly form