Not Equivalent in LaTeX (\not\equiv)

Where it is used

Slashed triple bar: not congruent modulo n, or not identically equal.

Number theory writes a \not\equiv b \pmod{n} when n does not divide a - b, for example in Fermat's little theorem hypothesis a \not\equiv 0 \pmod{p}. The \not prefix overlays a slash on the relation; place it immediately before \equiv. In some fonts the slash looks slightly off-center, but there is no standard dedicated glyph among the common symbol fonts, so \not\equiv is the usual choice. In logic it means not logically equivalent. For simple inequality, use \neq instead.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Not Equivalent: $\not\equiv$

\[ a \not\equiv 0 \pmod{p} \implies a^{p-1} \equiv 1 \pmod{p} \]
\end{document}

Related symbols

• Equivalent\equiv
• Square\square
• Tautology (verum, top)\top
• Contradiction (falsum, bottom)\bot
• Because\because
• Therefore\therefore

Frequently asked questions

How do I write Not Equivalent in LaTeX?

Type \not\equiv in math mode, for example $a \not\equiv 0 \pmod{p} \implies a^{p-1} \equiv 1 \pmod{p}$. It works in plain LaTeX without loading any package.

Which package do I need for \not\equiv?

None. \not\equiv is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \not\equiv in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\not\equiv$ in running text. If you only need the glyph in text, paste the Unicode character ≢ instead (with XeLaTeX or LuaLaTeX and a font that has it).