Question: Prove that for all integers n , it is the case that n is even if and only if 3 n is even. That is

Prove that for all integers n, it is the case that n is even if and only if 3n is even. That is, prove both implications: if n is even, then 3n is even, and if 3n is even, then n is even.
Hint.
Prove that for all integers n , it is the case

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