OK: prove "If n is an odd integer, then there exists an integer x such that n = 4x + 1 or n = 4x + 3.

I could also prove its negation, which is: For some integer x such that n is odd and for all integer x, n doesn't equal 4x + 1 and n doesn't equal 4x + 3.

So I start off with: Let n = 2k + 1 for some integer k.

Then I'm stuck ... lol

(I wanna prove the first, because I feel as though it would be easier) - but how do I show 2k + 1 = 4x + 1 or 4x + 3???