The parity of an integer describes whether or not it is divisible by 2. We say that

In general, even numbers take the form n=2k, and odd numbers take the form n=2k+1 for some k∈Z.

Example

Prove that if n2 is even, n must be even.

Suppose that there exists an integer n such that n2 is even but n is odd.

That means n=2k+1 for some k∈Z, from which it follows that:

But collecting factors of 2 shows:

which is the definition of an odd number. This is a contradiction, since n2 was given to be even.

Hence, by contradiction, if n2 is even that n is even. Q.E.D.