Suppose that a and b are integers, a ≡ 4 (mod 13), and b ≡ 9 (mod 13).

Find the integer c with 0 ≤ c ≤ 12 such that

a) c ≡ 9a (mod 13).

b) c ≡ 11b (mod 13).

c) c ≡ a + b (mod 13).

d) c ≡ 2a + 3b (mod 13).

e) c ≡ a² + b² (mod 13).

f ) c ≡ a³ − b³ (mod 13).