Question 5
Determine all integers $n \ge 1$ for which there exists $n$ real numbers $x_1, x_2, \dots, x_n$ in the closed interval $[-4, 2]$ such that the following three conditions are fulfilled:
- the sum of these real numbers is at least $n$;
- the sum of their squares is at most $4n$;
- the sum of their fourth powers is at least $34n$:
- the sum of these real numbers is at least $n$;
- the sum of their squares is at most $4n$;
- the sum of their fourth powers is at least $34n$: