Question

Prove that n^2 +6n is even, then n is even

Answer 1

Answer:

Suppose that n is not even, that is, n is odd. Then n = 2k + 1 for some integer k. So n2 = (2k +1)2 = 4k2 + 4k + 1 = 2 (2k2 + 2k) + 1 which is odd. Thus we have proved: if n is not even, then n2 is not even.