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## IMC 2012 Problem 9

Let ${n \geq 2}$ be an integer. Find all real numbers ${a}$ such that there exist real numbers ${x_1,..,x_n}$ satisfying

$\displaystyle x_1(1-x_2)=x_2(1-x_3)=...=x_{n-1}(1-x_n)=x_n(1-x_1)=a.$