Proving divisibility question using contradiction

Question:

For any integer n, (n^2 - 2) is not divisible by 4 ... Prove by contradiction

__Proof:__ Suppose the contrary, that is for any integer m, (m^2 - 2) is divisible by 4. By definition of divide, n = dk. Thus (m^2 - 2) = 4k.

i don't know how to finish this. i know that if n squared is even then n is even (long way is n=2k for even, n=2k+1 for odd) and n has to be even and greater than 2 for my thus statement to be true. just can't quite piece it together.