If nn and mm are integers and n2+m2n2+m2 is even, which of the following is impossible?

Given:
n and m are integers
n² + m² is even.

Choices:
a) n and m are even
b) n and m are odd
c) n + m is even
d) n + m is odd
e) none of these are impossible.

let us assume:
n and m are even. 2² + 4² = 4 + 16 = 20 even.
n and m are odd. 3² + 5² = 9 + 25 = 34 even
n + m is even : 2 + 4 = 6 ; 3 + 5 = 8 even

Using the assumption as basis, D.) n + m is odd  is impossible.