Proof By Contradiction where p always proves q true

Question

Prove that for any even integer n, n^2 mod 2 = 0 using proof by contradiction. (Question)

• Let p: any even integer n
• Let q: n^2 mod 2 = 0

In this example, if proved by contradiction, I'll be assuming ~(p → q) = p ∧ ~q = true.

With this, ~q can never be proven at all so long as p remains. How do I solve this question via proof by contradiction then?

Would doing ~p and ~q be the same? This would seem like inverse (~p → ~q) or contrapositive (~q → ~p) instead.