Question 90
Find all positive integers $n \ge 4$ for which the following property holds true: *any distinct and nonzero complex numbers $a, b, c$, satisfying
$$
(a - b)^n + (b - c)^n + (c - a)^n = 0,
$$
are the complex coordinates of the vertices of an equilateral triangle.*
$$
(a - b)^n + (b - c)^n + (c - a)^n = 0,
$$
are the complex coordinates of the vertices of an equilateral triangle.*