Now, the step. You gotta write the inductive hypothesis, in order to have it in mind. Because there's a probability of 99.9% that you'll use it.
We want to prove that if is a multiple of 3, then is one too.
So we start from
As it is written, it's equal to
Now, you know that is a multiple of 3. It's time to use it here. So let's write
By expanding, we get :
3 is obviously a multiple of 3 and is a multiple of 3, according to the inductive hypothesis. The induction is proved.
Another way of doing it is to assume that , k an integer. And thus