# Isn't this USAMO 2017 Problem 6

Algebra Level 3

Let $$S$$ be the maximum possible value of $\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4}$given that $$a$$, $$b$$, $$c$$, $$d$$ are nonnegative real numbers such that $$a+b+c+d=4$$. Given that $$S$$ can be written in the form $$\frac{m}{n}$$ where $$m,n$$ are coprime positive integers, find $$100m+n$$.

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