A residue class is a set of integers that share the same remainder when divided by a specific integer, known as the modulus. For example, when dividing by 5, the residue classes are 0, 1, 2, 3, 4. Each integer belongs to one of these classes based on its remainder. In mathematical terms, if we have an integer a and a modulus n , the residue class of a modulo n is denoted as [a]_n . This concept is fundamental in number theory and is used in various applications, including cryptography and computer science.