UA-UMO 1997 Problem 106

Solve in the real numbers the system:

$x_1+x_2+...+x_{1997}=1997,$

$x_1^4+x_2^4+...+x_{1997}^4=x_1^3+x_2^3+...+x_{1997}^3.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.