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,$$c_1+c_2+ ... +c_n=0,$$
c_1^2+c_2^2+ ... +c_n^2=0,$$c_1^2+c_2^2+ ... +c_n^2=0,$$
c_1^3+c_2^3+ ... +c_n^3=0,$$c_1^3+c_2^3+ ... +c_n^3=0,$$
.... .... ....$$.... .... ....$$
c_1^n+c_2^n+ ... +c_n^n=0.$$c_1^n+c_2^n+ ... +c_n^n=0.$$
The question is: Is the trivial solution the only solution to the system?
