International Mathematical Olympiad 1995 Problem 3

Determine all integers $n > 3$ for which there exist $n$ points $A_1, \ldots, A_n$ in the plane, no three collinear, and real numbers $r_1, \ldots, r_n$ such that for $1 \leq i < j < k \leq n$, the area of $\triangle A_i A_j A_k$ is $r_i + r_j + r_k$.