# Callous Constraint

Algebra Level 5

Positive reals $$x$$, $$y$$, and $$z$$ are such that $$\ x^3 + y^3 + z^3 = \left(3 + \dfrac{1}{666}\right)xyz$$.

Find the smallest integer value of $$k$$ satisfying the following inequality:

$\large \dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x} \ge 3+\dfrac{1}{k}.$

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