In its most basic form, modular arithmetic, also known as modulus arithmetic or clock arithmetic, is arithmetic performed with a count that resets itself to zero whenever a certain whole number N greater than one, or the modulus (mod), is reached.

The relationship is expressed symbolically as a ☰ b (mod n)

Equivalent ways of stating the relationship of congruence include:

• a leaves a remainder of b when divided by n

• a = tn + b for some integer t