I wrote a proof and I'm really just here to make sure my argument is making sense.
For all x>=0, (x^2)-x is even. Base case: x=0. (0^2)-0 is even. Inductive Step: x>= 0. Suppose (x^2)-x is even. Then there is an integer y so that (x^2)-x = 2y Now (x+1)^2 - (x+1) = x^2 +2x + 1 - x - 1. = x^2 + x = (x^2 - x) + 2x = 2y + 2x = 2(y+x) Thus it's even.
Does that argument make sense? It checks out to me..