Question: Suppose that a and b are integers, a 4 (mod 13), and b 9 (mod 13). Find the integer c with 0

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).

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