Question 132
Let $A = \{a_1, a_2, \ldots, a_{2010}\}$ and $B = \{b_1, b_2, \ldots, b_{2010}\}$ be two sets of complex numbers, such that the equality
$$
\sum_{1 \le i \lt j \le 2010} (a_i + a_j)^n = \sum_{1 \le i \lt j \le 2010} (b_i + b_j)^n
$$
holds for every $n = 1, 2, \ldots, 2010$. Prove that $A = B$.
$$
\sum_{1 \le i \lt j \le 2010} (a_i + a_j)^n = \sum_{1 \le i \lt j \le 2010} (b_i + b_j)^n
$$
holds for every $n = 1, 2, \ldots, 2010$. Prove that $A = B$.