Equivalent / identical (≡) in LaTeX

Q: How do I write a congruence mod n?

Combine \equiv with \pmod: $a \equiv b \pmod{n}$ renders with the proper spacing and brackets.

Q: What is the difference between \bmod, \pmod and \mod?

\bmod is the binary operator (5 \bmod 3); \pmod{n} adds '(mod n)' for congruences; \mod writes 'mod n' without parentheses.

\equiv produces the identically-equal / equivalence relation, used for identities that hold for all values and for congruence in modular arithmetic.

\equiv

LaTeX command

\equiv

Not the symbol you meant? Draw it to find the command →

\equiv has two everyday meanings. First, 'identically equal': \sin^2\theta + \cos^2\theta \equiv 1 asserts equality for every value of theta, not just a particular solution. Second, congruence in modular arithmetic, written $a \equiv b$ \pmod{n}.

For the modular use, \pmod{n} supplies the parentheses and correct spacing, giving '(mod n)'. Its relatives are \bmod, the binary operator as in $7 mod 3$ , and \mod, which writes 'mod $n^{'}$ without brackets. \bmod and \pmod are built into LaTeX; \mod comes from amsmath.

The symbol also appears for logical equivalence (where \iff is an alternative) and occasionally for definitions (where := via \coloneqq is common). Its negation is \not\equiv; there is no standard single command for it.

Examples

a \equiv b (mod n)

$a \equiv b \pmod{n}$

congruence modulo n

17 \equiv 2 (mod 5)

$17 \equiv 2 \pmod{5}$

a numeric congruence

sin^{2} θ + cos^{2} θ \equiv 1

$\sin^2\theta + \cos^2\theta \equiv 1$

an identity for all theta

f (x) \equiv 0

$f(x) \equiv 0$

the identically-zero function

P \equiv Q

$P \equiv Q$

logical equivalence

Tips and common mistakes

For modular arithmetic use \pmod{n}, which adds the parentheses and spacing: $a \equiv b$ \pmod{n}.
Use \bmod for the binary operator ( $7 mod 3$ ) and \mod for 'mod $n^{'}$ without parentheses.
Distinguish identically-equal (true for every value) from ordinary = (true for the values in question).
Do not use \equiv for 'approximately'; that is \approx.
The negation is \not\equiv; there is no dedicated single command.

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FAQ

What does \equiv mean in LaTeX?

It prints the triple-bar sign, meaning 'identically equal to' (true for every value) or 'congruent to' in modular arithmetic, depending on context.

How do I write a congruence mod n?

Combine \equiv with \pmod: $a \equiv b (mod n)$ renders with the proper spacing and brackets.

What is the difference between \bmod, \pmod and \mod?

\bmod is the binary operator ( $5 mod 3$ ); \pmod{n} adds '(mod n)' for congruences; \mod writes 'mod $n^{'}$ without parentheses.

Equivalent / identical (≡) in LaTeX

Examples

Tips and common mistakes

Working from handwritten notes?

FAQ

See also