Suppose that a and b are integers, a ≡ 11 (mod 19), and b ≡ 3 (mod 19). Find the integer c with 0 ≤ c ≤ 18 such that

a) c ≡ 13a (mod 19).

b) c ≡ 8b (mod 19).

c) c ≡ a − b (mod 19).

d) c ≡ 7a + 3b (mod 19).

e) c ≡ 2a² + 3b² (mod 19).

f) c ≡ a³ + 4b³ (mod 19).