Use a direct proof: The sum of an integer and its square is even.

Answer 1

First, it is proven that the product of odd times even is even...

To show this, 2t(2t+1) is clearly even for odd integer 2t+1 and even integer 2t

N +N^2 = N(N+1)

if N is even, then N+1 is odd and the product is therefore even.

If N is odd, then N+1 is even and the product is therefore even.

end of proof