a) Prove the cancelation law for congruences: If ax ≡ ay (mod m) and gcd(a,m) = 1 then x ≡ y (mod m), by making use of the multiplicative inverse of a.
b) Show that the cancelation law fails if gcd(a,m) > 1 by considering the example 6x ≡ 6y (mod 8). (That is, show there is a solution with x ≠ y (mod 8).)