Question 16
a) Does there exist an integer $c$ and a polynomial $P(x)$ with integer coefficients for which $P(c) \neq c$, but $P(P(c)) = c$?
b) Does there exist an integer $c$ and a polynomial $P(x)$ with integer coefficients for which $P(c) \neq c$ and $P(P(c)) \neq c$, but $P(P(P(c))) = c$?
b) Does there exist an integer $c$ and a polynomial $P(x)$ with integer coefficients for which $P(c) \neq c$ and $P(P(c)) \neq c$, but $P(P(P(c))) = c$?