Let n be a positive integer, and c_1, c_2, ... c_n be (unkown) real numbers .

Consider the system

$$c_1+c_2+ ... +c_n=0,$$

$$c_1^2+c_2^2+ ... +c_n^2=0,$$

$$c_1^3+c_2^3+ ... +c_n^3=0,$$

$$.... .... ....$$

$$c_1^n+c_2^n+ ... +c_n^n=0.$$

The question is: Is the trivial solution the only solution to the system?