Given pairwise distinct numbers $c_1, c_2, \dots c_n \in \mathbb{C} \setminus \{0\}$, does the system of equations $$\frac{6}{c_k} + \sum_{i \ne k} \frac{2}{c_k  c_i} = \sum_{i = 1}^n \frac{1}{c_k  x_i}, \ k = 1,2,3, \dots, n$$ have a nontrivial solution $(x_1, x_2, \dots, x_n) \in \mathbb C^n$?
