INMO 2016 proposal from IISc

Algebra Level 5

\[\begin{align} f(x) & \le 2(1+x) & \forall x \in [1, \infty) \\ x f (x+1) & = (f(x))^2 - 1 & \forall x \in [ 1,\infty ) \end{align} \]

A function \(f:[1, \infty) \rightarrow [1, \infty) \) satisfy the conditions above. Find \(f(2016)\).

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