Question 76
A polynomial $x^2 + 1$ is written on the blackboard. Every day Kate wipes off currently written polynomial $F(x)$ and writes one of the $F^2(x) + 1$ and $F(x^2 + 1)$ instead, choosing at her discretion. Prove that the constant (free) term will exceed $2^{2^{222}}$ in one year.
(Arseniy Nikolaev)
(Arseniy Nikolaev)