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IMO LongList 1967, Bulgaria 5

Source: IMO LongList 1967, Bulgaria 5

December 16, 2004
linear algebramatrixalgebrapolynomialsystem of equationsIMO ShortlistIMO Longlist

Problem Statement

Solve the system of equations: x2+x−1=yy2+y−1=zz2+z−1=x. \begin{matrix} x^2 + x - 1 = y \\ y^2 + y - 1 = z \\ z^2 + z - 1 = x. \end{matrix}
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