Note that [tex]a^2-a=a(a-1)[/tex], so that [tex]a^2-a[/tex] is the product of two consecutive integers. This means one of them must be even, and the other is odd. The product of an odd number and an even number is itself an even number, so [tex]2\mid a^2-a[/tex] for any integer [tex]a[/tex].
