Question: Prove that for all integers n, (-n) mod 2 = n mod 2. Give an example to show that it is not always true that

Prove that for all integers n, (-n) mod 2 = n mod 2. Give an example to show that it is not always true that (-n) mod 3 = n mod 3.

Professor mentioned to prove for odd and even integers, however, I don't know how to start the proof.

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