Prove for all M and N, if M and M-N are even, then N is even.
Assume, by contradiction, that is odd. Then, for some
We also know that for some . Then, which is an odd number, thus is odd, in contradiction, and so N is even.
Prove for all M and N, if M and M-N are even, then N is even.
Do you know that sum or substraction of even numbers is even? If you can't use (or don't know) this then prove it: it's trivial when we characterize an even number as 2k , where k is an integer.