A set of m integers which are distinct mod m is sometimes called a

complete residue set mod m. Show that, mod 11, {O, 1,2,22, ... ,29 } is a complete residue set, but {02, 12,22, ... , 102} is not.

If {al, a2,"" am} is a complete residue set mod m, and gcd(k, m) = 1, then so is {kaI, ka2, ... , kam}. Prove this.