Question 3
Determine all integers $n\gt 3$ such that there are $n$ points $A_1,A_2,\ldots,A_n$ in the plane that satisfy the following two conditions simultaneously:
(a) No three lie on the same line.
(b) There exist real numbers $p_1,p_2,\ldots,p_n$ such that the area of $\triangle A_iA_jA_k$ is equal to $p_i+p_j+p_k$, for $1\le i\lt j\lt k\le n$.
(a) No three lie on the same line.
(b) There exist real numbers $p_1,p_2,\ldots,p_n$ such that the area of $\triangle A_iA_jA_k$ is equal to $p_i+p_j+p_k$, for $1\le i\lt j\lt k\le n$.