Math proof question on right triangle?

so using Pythagorean Theorem, we see that (m+1)^2+m^2=a^2 meaning 2m^2+2m+1=a^2. From that we know 2m^2+2m MUST be even. So 2m^2+2m+1 must be odd. And any odd number squared is also odd, hence a is odd.