Symbols:Number Theory/Congruence

Congruence

$\equiv$

Let $x, y \in \R$.

Then $x$ is congruent to $y$ modulo $z$ if and only if their difference is an integer multiple of $z$:

$x \equiv y \pmod z \iff \exists k \in \Z: x - y = k z$

The $\LaTeX$ code for \(x \equiv y \pmod z\) is x \equiv y \pmod z .

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $7$: Common signs and symbols: identity, congruence modulo $n$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols