Determine all real solutions to the system of equations: $$x_1 + x_2 +...+ x_{2004 }= 2004$$$$x^4_1+ x^4_2+ ... + x^4_{2004} = x^3_1+x^3_2+... + x^3_{2004}$$
Source: 2004 Cuba MO 2.1
Tags: algebra, system of equations, System
Determine all real solutions to the system of equations: $$x_1 + x_2 +...+ x_{2004 }= 2004$$$$x^4_1+ x^4_2+ ... + x^4_{2004} = x^3_1+x^3_2+... + x^3_{2004}$$