Question 183
Let $a_1, a_2, ..., a_n$ be positive integers, not necessarily distinct but with at least five distinct values. Suppose that for any $1 \le i \lt j \le n$, there exist $k, \ell$, both different from $i$ and $j$ such that $a_i + a_j = a_k + a_\ell$. What is the smallest possible value of $n$?