Hello !

Don't forget the first case, that is for

Now, the step. You gottawritethe 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

Then