Elementary Proof: Let $x$ be an integer. If $4|x^2$, then $4|x$

Question

All I have so far is pretty much the definition:

$x^2=4a$

Doing the square root doesn't seem to help, so I thought about using the contrapositive approach, but how would you say that $x$ doesn't divide $4$, definition-wise? Something with congruence?

Answer 1

$x=2$ is a counter-example. $4\mid 2^2=4,$ but $4\not\mid 2$