If n and m are integers and n2m2 is even which of the follow

If n and m are integers and n^2+m^2 is even, which of the following is impossible?

Solution

Since n^2+m^2 is even, either both n^2 and m^2 are even, or they are both odd. Therefore, n and m are either both even or both odd, since the square of an even number is even and the square of an odd number is odd. As a result, n+m must be even.