Can someone help me with this proof

Question

Prove that, for any integer $n$, if $n-2$ is divisible by $4$,then $n^2-4$ is divisible by $16$.

*I don't know what kind of method to use.

Answer 1

Hint:

$$n^2-4=(n-2)(n-2+4)=(n-2)^2+4(n-2)$$

Answer 2

You are told that $n-2$ is divisible by $4$, which means that there exists an integer $k$ such that $n-2=4k$.

And now it's easy:

$n-2=4k\implies n=4k+2\implies n^2-4=(4k+2)^2-4=\ldots$ what?