Question 106
Let us consider a polynomial $P(x)$ with integer coefficients satisfying
$$
P(-1) = -4, \quad P(-3) = -40, \quad \text{and} \quad P(-5) = -156.
$$
What is the largest possible number of integers $x$ satisfying
$$
P(P(x)) = x^2?
$$
$$
P(-1) = -4, \quad P(-3) = -40, \quad \text{and} \quad P(-5) = -156.
$$
What is the largest possible number of integers $x$ satisfying
$$
P(P(x)) = x^2?
$$