Still a bit rusty on proofs by contraposition Would someone

Still a bit rusty on proofs by contraposition. Would someone mind to help me please?

The question is:

If the sum of three integers is even then at least one of the integers is even

How do you prove this using contraposition?

Solution

If neither integer is even, then the product is not even.
That is, the product of two odd integers is odd. This is easily verified from considering the equality

(2k+1)(2m+1)=4km+2k+2m+1=2(2km+k+m)+1