An equivalence class for the equivalence relation of congruence modulo n. So, two integers are in the same class if they have the same remainder upon division by n. If [a] denotes the residue class modulo n containing a, the residue classes modulo n can be taken as , , ,…, [n−1]. The sum and product of residue classes can be defined by
[a] + [b] = [a + b], [a][b] = [ab],
where it is necessary to show that the definitions here do not depend upon which representatives a and b are chosen for the two classes. With this addition and multiplication, the set, denoted by Zn, of residue classes modulo n forms a ring (in fact, a commutative ring with identity). If n is composite, the ring Zn has divisors of zero, but when p is prime Zp is a field.