Let $k \geq 2$ be a D5094: Positive integer.

Then \begin{equation} \# \left\{ (n, m) \in \mathbb{Z} \times \mathbb{Z} : 1 \leq m \leq n \text{ and } \binom{n}{m} = k \right\} = O_{n \to \infty}(1) \end{equation}