Show that n(n + 2)(n + 4) is either divisible by 16, or is an odd number. I understand more or less how to do this problem, however, I am having trouble actually showing that n can be divisible by 16.
Here's what I have done so far
If n is an odd integer, then n = 2k + 1, where k is any integer.
2k + 1 * (2k + 3) * (2k + 5) must be an odd number (due to multiply odd numbers)
If n is an even integer, then n = 2k, where k is any integer.
2k * (2k + 2) * (2k + 4)
How do I show that 2k * (2k + 2) * (2k + 4) is a multiple of 16?

For the divisible by 16 case, note that n,n+2,n+4, contains at least 1 multiple of 4, being consecutive even numbers.
