Prove each of the following assertions:
(a) If a ≡ b (mod n) and m | n, then a ≡ b (mod m).
(b) If a ≡ b (mod n) and c > 0, then ca ≡ cb (mod cn).
(c) If a ≡ b (mod n) and the integers a, b, n are all divisible by d > 0, then a/d ≡ b/d (mod n/d).
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