Question 38
Determine all integers $n$ for which there are positive real numbers $0 \lt a_{1} \leq a_{2} \leq \ldots \leq a_{n}$
$$
\sum_{k=1}^{n} a_{k}=96, \quad \sum_{k=1}^{n} a_{k}^{2}=144, \quad \sum_{k=1}^{n} a_{k}^{3}=216
$$
$$
\sum_{k=1}^{n} a_{k}=96, \quad \sum_{k=1}^{n} a_{k}^{2}=144, \quad \sum_{k=1}^{n} a_{k}^{3}=216
$$