n^2+n = odd

[math_celebrity]

n^2+n = odd

Factor n^2+n:
n(n + 1)

We have one of two scenarios:

1. If n is odd, then n + 1 is even. The product of an odd and even number is an even number
2. If n is even, then n + 1 is odd. The product of an even and odd number is an even number