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**Jhevon** to prove using the contrapositive method means the following.

by the contrapositive method, we prove a statement $\displaystyle P \implies Q$ by showing $\displaystyle \neg Q \implies \neg P$

so start by assuming $\displaystyle m \ne n$, where does this get you? how does this cause $\displaystyle m^2$ to relate to $\displaystyle n^2$? will they be equal?

Hint: we say an integer is even if it can be expressed as $\displaystyle 2n$ for $\displaystyle n \in \mathbb{Z}$. now note that $\displaystyle -2n = 2(-n)$