Prove that n^3+2n is divisible by 3.
Case 1: n = 1
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.