mod

Represents the modulo operation or congruence relation in number theory and computer science.

Overview

Essential for expressing arithmetic relationships between numbers with respect to a given modulus, particularly in number theory, cryptography, and computer programming.

Commonly used to describe clock arithmetic and cyclic patterns
Fundamental in expressing congruence relations between integers
Critical for algorithms involving periodic behavior or wrap-around operations
Frequently appears in discrete mathematics and computational problems

Examples

Expressing congruence modulo in number theory

3 \equiv 5 \mod 2

3 \equiv 5 \mod 2

Showing multiple equivalent numbers in modular arithmetic

15 \equiv 3 \equiv -1 \mod 7

15 \equiv 3 \equiv -1 \mod 7

Solving a linear congruence equation

2x \equiv 4 \mod 6

2x \equiv 4 \mod 6