Question 52
For each integer $n \gt 1$, find a set of $n$ integers $\{a_1, a_2, \dots, a_n\}$ such that the set of numbers $\{a_i + a_j \mid 1 \le i \le j \le n\}$ leave distinct remainders when divided by $n(n+1)/2$. If such a set of integers does not exist, give a proof.