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Part of 2001 Grosman Memorial Mathematical Olympiad

Problems(1)

x_1 +x_2 +...+x_{2000} = 2000, x_1^4 +...+x_{2000}^4= x_1^3 +...+x_{2000}^3

Source: Israel Grosman Memorial Mathematical Olympiad 2001 p1

2/15/2020
Find all real solutions of the system {x1+x2+...+x2000=2000x14+x24+...+x20004=x13+x23+...+x20003\begin{cases} x_1 +x_2 +...+x_{2000} = 2000 \\ x_1^4 +x_2^4 +...+x_{2000}^4= x_1^3 +x_2^3 +...+x_{2000}^3\end{cases}
system of equationsalgebra