I'm not sure where to start on this induction problem.

**Problem:** A group of $n \geq 1$ people can be divided into teams, each containing either 4 or 7 people. What are all possible values of $n$? Use induction to prove that your answer is correct.

This problem is similar to one where we prove that for all $n \geq 8$, $n$ was made up of multiples of 5 and 3. 

This is similar, but I haven't gotten far because I can't seem to decide on a base case. The question says that for $n \geq 1$, but a group of 1 person, or 2 or 3, can't be split up into multiples of 4 and 7. So I think that I need to find $n$ for which all numbers greater than $n$ are made up of multiples of 4 and 7.

For the 5's and 3's problem, the base case was 8, which is $5+3$, but that doesn't work for this, as 11 works, and 12 works but not 13. Again, I'm not sure where the base case is, so I don't know where to begin.

My induction hypothesis was the following: For all $n\geq 1$, $n$ is the sum of multiples of 4 and 7. That is, $4x + 7y = n$, where $x$ and $y$ are positive integers.