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)