Hey everyone, I have this problem for homework and got started on it when n is odd (easy). But can't figure out how to solve it when n is even:

Let n be an integer greater than or equal to 3. Prove that n^2 -1 is not prime.

So I split it into when n is odd and when n even.

ODD:

n = 2c + 1

n^2 - 1 = (2c + 1)^2 - 1

"" = 4c^2 + 4c + 1 - 1

"" = 2(2c^2 + 2c)

d = 2c^2 + 2c

"" = 2d

Therefore 2 | n^2 -1, so n^2 -1 isn't prime for odd numbers

But I can't figure out where to go from here for even n's. Any hints on how to think about this?