If (a mod n) = (b mod n), then a is **equivalent** to b, modulo n,
denoted a b (mod n).

An **equivalence class modulo n** containing an integer a

is [*a*]_{n} = {a + kn k Z}.

Example: if a=8, n=3, then q = 2, r = 2, and some
b a are 2, 5, 8, 11, 14, 17, ....

The equivalence classes modulo n are

[0]_{3} = {..., -3, 0, 3, 6, 9, 12, ...} =

[1]_{3} = {..., -2, 1, 4, 7, 10, 13, ...}

[2]_{3} = {..., -1, 2, 5, 8, 11, 14, ...}