Minimization

Algebra Level 3

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

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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