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 \(f(2016)\).
by
Priyanshu Mishra