Question 45
Let $n \gt 3$ be a positive integer and $P_1, P_2, \dots, P_n$ be different points on the plane such that all pairwise distances between them are integers and the distances $P_iP_1, P_iP_2, \dots, P_iP_n$ rearranged in non-decreasing order coincide for all $i = 1, 2, \dots, n$. Find all possible values of $n$.