I got to proof:
I am sorry for not typing this with LaTeX formatting, the backslash on my computer does not work (neither on the keyboard nor copied :s)
I see that
(n+(x*2n))*(m+(y*2m) where x,y in N & n,m are odd always gives an odd answer (odd*odd=odd)
That odd number is an even number + 1; hence 2x + 1, where 2x always give a black and a white square, and the one remaining is the one in the corner (white one)
Also I see that from any n/m to the next n/m is a step of 2 squares (black AND white), so there is still one more white than black square (since the first one is white.
But I cannot write this in formal language; and I got to.. Any Idea?