Minimization

Algebra Level 3

anb+c+bnc+a+cna+bC\frac{a^n}{b+c}+\frac{b^n}{c+a}+\frac{c^n}{a+b} \geq C

Given that a,ba,b and cc are positive real numbers satisfying a+b+c=3a+b+c=3, and nn is a positive integer. For all choices of a,b,ca,b,c and nn, what is the largest constant CC satisfying the inequality above?

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