Question 74
For which positive integers $n$, does there exist a sequence of real numbers $(x_{1}, x_{2}, \ldots, x_{n})$ such that
- $-2 \lt x_{i} \lt 2$ for all $i$,
- $x_{1} + x_{2} + x_{3} + \dots + x_{n} = 0$, and
- $x_{1}^{4} + x_{2}^{4} + x_{3}^{4} + \dots + x_{n}^{4} \geqslant 32$.
- $-2 \lt x_{i} \lt 2$ for all $i$,
- $x_{1} + x_{2} + x_{3} + \dots + x_{n} = 0$, and
- $x_{1}^{4} + x_{2}^{4} + x_{3}^{4} + \dots + x_{n}^{4} \geqslant 32$.