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Some training in systems of equations

Source: Bulgaria JBMO TST 2023, Day 2, Problem 1

June 17, 2023
algebrasystem of equationsAlgebraic Manipulations

Problem Statement

Determine all triples (x,y,z)(x,y,z) of real numbers such that x4+y3z=zxx^4 + y^3z = zx, y4+z3x=xyy^4 + z^3x = xy and z4+x3y=yzz^4 + x^3y = yz.
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