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3x3 system, x^y = z , y^z = x, z^x = y

Source: 1981 Swedish Mathematical Competition p2

March 28, 2021
system of equationsSystemalgebra

Problem Statement

Does {xy=zyz=xzx=y\left\{ \begin{array}{l} x^y = z \\ y^z = x \\ z^x = y \\ \end{array} \right. have any solutions in positive reals apart from x=y=z=1x = y = z= 1?
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