Residue Classes

Abstract

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 (mod 6)1^2=1 (mod 6)2^2=4 (mod 6)3^2=3 (mod 6)4^2=4 (mod 6)5^2=1 (mod 6) are all the possible residues. A complete residue system is a set of integers containing one element from each class, so {0,1,9,16} would be a complete residue system for x^2 (mod 6). The phi(m) residue classes prime to m form a group under the...