Let $a \in [0, \infty)$ be an D4767: Unsigned real number.

Then \begin{equation} \frac{1}{N} (a, a, \ldots, a) = \underset{x \in [0, \infty)^N : \sum_{n = 1}^N x_n = a}{\text{arg max}} \, \prod_{n = 1}^N x_n \end{equation}