Prove Let n be a natural number Any set of n integers a1 a2

Prove. Let n be a natural number. Any set of n integers {a1, a2, . . . , an} for which no two are congruent modulo n is a complete residue system modulo n.

Solution

There are n distinct residues in complete residue system

Since given set have n integers and no two are congruent modulo n hence we have a set of n distinct residues modulo n.

ANd hence the given set is a complete residue system modulo n