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Part of 2013 Federal Competition For Advanced Students, Part 1

Problems(1)

Cyclic Equations in x,y,z

Source: Austrian Federal Competition 2013, part 1, problem 2

6/18/2013
Solve the following system of equations in rational numbers: (x2+1)3=y+1,(y2+1)3=z+1,(z2+1)3=x+1. (x^2+1)^3=y+1,\\ (y^2+1)^3=z+1,\\ (z^2+1)^3=x+1.
algebrapolynomialfunctionRational Root TheoremAustria2013AUT