Let $a \in (0, \infty)$ be a D5407: Positive real number.

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