The question is:
Prove the statement or disprove it using a counterexample. If $2a^2 = b^2$, where $a,b\in \mathbb Z$, then $2$ is a common divisor of $a$ and $b$?
The only thing that works in this case is when $a=b=0$. And $2$ is a common divisor of $0$ . I'm not quite sure if that's a valid proof.