Question 112
Determine all integers $n \ge 3$ satisfying the following condition: there exist pairwise distinct real numbers $a_1, a_2, \dots, a_n$ such that the $\frac{1}{2}n(n-1)$ sums $a_i+a_j$, $1 \le i \lt j \le n$, ordered increasingly, form an arithmetic sequence (the difference of every two consecutive sums is the same).