# Tasty problem to be digested

Algebra Level 4

$\large \sum_{\text{cyc}} \frac {x^3}{1 - x^8}$

If $$x$$, $$y$$ and $$z$$ are positive numbers such that $$x^4 + y^4 + z^4 = 1$$, find the minimum value of the sum above.

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