# Minimization

Algebra Level 4

$\frac{a^n}{b+c}+\frac{b^n}{c+a}+\frac{c^n}{a+b} \geq C$

Given that $$a,b$$ and $$c$$ are positive real numbers satisfying $$a+b+c=3$$, and $$n$$ is a positive integer. For all choices of $$a,b,c$$ and $$n$$, what is the largest constant $$C$$ satisfying the inequality above?

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