We're going to try this with LaTeX and hope for the best.

Case 1: n = 1

Check!

Now assume the theorem is true for n = k. We need to show it is true for n = k + 1. So we assume

where a is an integer.

Thus we need to show the same for

The first term is divisible by 3 due to our assumption at n = k. The second term is obviously divisible by 3.

etc, etc.

-Dan