residue

Number theory is a branch of mathematics focused on the properties of positive integers. While historically considered a pure field with no real-world applications, the development of computers and digital communication has revealed its practical uses, particularly in areas like cryptography.

A key concept within number theory is modular arithmetic, which involves calculations with remainders after division by a fixed number called the modulus. This leads to the idea of residue classes, where numbers are grouped based on the remainder they leave when divided by the modulus. For example, in modular arithmetic with a modulus of 5, numbers like 2, 7, and 12 all belong to the same residue class because they leave a remainder of 2 when divided by 5.1234