International Mathematical Olympiad 1999 Problem 2

Let $n$ be a fixed integer, with $n \geq 2$.

(a) Determine the least constant $C$ such that the inequality

$$\sum_{1 \leq i < j \leq n} x_i x_j (x_i^2 + x_j^2) \leq C \left( \sum_{1 \leq i \leq n} x_i \right)^4$$

holds for all real numbers $x_1, \ldots, x_n \geq 0$.

(b) For this constant $C$, determine when equality holds.