So, can I just put x times x is not a multiple of 2? Does that solve the problem?
LEMMA: (a) an odd integer times an odd integer is odd
............(b) an odd integer times an even integer is even
............(c) an even integer times an even integer is even
i leave the proof of the lemma to you (or just part (a) of the lemma, since that is what you are dealing with here )
now, we can make our indirect proof run smoothly.
Claim: if is even, then is even
By the contrapositive, we need to show that if is odd, then is odd. This is a direct consequence of Lemma (a)
EDIT: Ah, i just saw Reckoner's nice solution. pick your favorite.