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System of equations

Source: Finnish Mathematics Competition 2005, Final Round, Problem 3

November 14, 2011
absolute valuealgebra unsolvedalgebra

Problem Statement

Solve the group of equations: {(x+y)3=z(y+z)3=x(z+x)3=y\begin{cases} (x + y)^3 = z \\ (y + z)^3 = x \\ (z + x)^3 = y \end{cases}
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