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X^3 - 4x^2 - 16x + 60 = y, ...

Source: German Math. Competition BWM 2003, 1st round, problem 2

November 19, 2005
functionalgebrasystem of equationsalgebra proposed

Problem Statement

Find all triples (x, y, z)\left(x,\ y,\ z\right) of integers satisfying the following system of equations: x3−4x2−16x+60=yx^3-4x^2-16x+60=y; y3−4y2−16y+60=zy^3-4y^2-16y+60=z; z3−4z2−16z+60=xz^3-4z^2-16z+60=x.
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