Question 5
For each integer $n>1$, find a set of $n$ integers $\{a_1,a_2,\ldots,a_n\}$ such that the set of numbers $\{a_i+a_j\mid1\le i\le j\le n\}$ leave distinct remainders when divided by $n(n+1)/2$. If such a set of integers does not exist, give a proof.