# RMO 2014

Algebra Level 4

Let $$x_{1}, x_{2}, \ldots , x_{2014}$$ be positive real numbers such that $$\displaystyle \sum_{j = 1}^{2014}x_{j} = 1$$. Determine the smallest constant $$K$$, such that $K \displaystyle\sum_{j = 1} ^ {2014} \dfrac{ x^2_{j} }{ 1 - x_{j} } \ge 1.$

###### This problem is taken from RMO 2014.
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