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x^3 + 3y^3 + 9z^3 - 9xyz = 0 in rationals

Source: 1983 Hungary - Kürschák Competition p1

October 10, 2022
algebrarational

Problem Statement

Let x,yx, y and zz be rational numbers satisfying x3+3y3+9z3−9xyz=0.x^3 + 3y^3 + 9z^3 - 9xyz = 0. Prove that x=y=z=0x = y = z = 0.
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