Modulus

A Binary Operation that returns the remainder of $\frac{a}{b}$

Definition

$z=ax+b$:

• $a$ is the quotient
• $b$ is $z\mathrm{mod}x$ or the remainder

Properties of Modular Arithmetic

Addition

• $((a\mathrm{mod}n)+(b\mathrm{mod}n))\mathrm{mod}n=(a+b)\mathrm{mod}n$

Multiplication

• $((a\mathrm{mod}n)\times (b\mathrm{mod}n))\mathrm{mod}n=(a\times b)\mathrm{mod}n$