Complete Residue System

Complete Residue System 

Any set of integers containing one representative from each number class modulo m (two integers a and b belong to the same class modulo m if a – b is divisible by m) is said to be a complete residue system modulo m. The most frequently used complete residue systems are the system of smallest positive residues 0, 1, 2, …, m – 1 and the system of absolutely smallest residues: – (m – 1)/2, …, -1, 0, 1, …, (m - 1)/2 for odd m and -m/2, – 1, 0, 1, …, m/2 – 1 for even m. Any m numbers that belong to different residue classes modulo m form a complete residue system modulo m.