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RMO 2016

Algebra Level 2

Let \(a\), \(b\), and \(c\) be positive real numbers such that

\[ \frac{a}{1+b} + \frac{b}{1 + c} + \frac{c}{1 + a} = 1.\]

What is the maximum value of \(abc?\)

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by Sayantan Saha

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