MathNet 2023-part-05 — 191 problems (EN–VI) Question 57

Determine the continuous functions $f : \mathbb{R} \to \mathbb{R}$ with the properties $f(1) = e$ and $f(x + y) = e^{3xy} \cdot f(x) \cdot f(y)$, for all $x, y \in \mathbb{R}$.