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.