# Anyone know the contest this is from? [closed]

Evidently the problem is to show this is impossible: $$\frac{z^3}{x^3+y^3+2xyz}=3$$$(x,y,z\in \mathbb N)$

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Why there isn't any solution in positive integers for $z^3 = 3(x^3 +y^3+2xyz)$?

A complete solution was given in comment by duje after my answer, elliptic curves.