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The following expression is given: $$\frac{x^7+y^7+z^7}{xyz(x^4+y^4+z^4)}$$

Simplify it, knowing that $x+y+z=0$.

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    Use that $z=-(x+y)$ and substitute and suffer for a bit. I think you should get a nice answer :)2012-03-02
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    @Victor: Diophantine equations? There is no equation and $x,y,z$ can be real/complex. contest-math? How do you know? I am removing those tags.2012-03-02

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