Question 3
I 3 (SWE 3), IMO6
Let $P(x)$ be a polynomial with integer coefficients. If $n(P)$ is the number of (distinct) integers $k$ such that $P^2(k)=1$, prove that
$$n(P)-\deg(P)\le2,$$
where $\deg(P)$ denotes the degree of the polynomial $P$.
Let $P(x)$ be a polynomial with integer coefficients. If $n(P)$ is the number of (distinct) integers $k$ such that $P^2(k)=1$, prove that
$$n(P)-\deg(P)\le2,$$
where $\deg(P)$ denotes the degree of the polynomial $P$.