In a school, there are $m$ teachers and $n$ students. We assume that each teacher has exactly $k$ students, and each student always has exactly $\ell$ teachers. Determine a relation between $m, n, k, \ell$.
Let $I$ denote the number of teacher-student relationships, then

$$
I=n \times \ell \quad \text { and } \quad I=m \times k
$$

and therefore $n \times \ell=m \times k$.