Chapter 4, Problem 23SE

Prove that if f(x) is a nonconstant polynomial with integer coefficients, then there is an integer y such that f(y) is composite. [Hint: Assume that $f\left(x_{\text{0}}\right)\text{=}p$ is prime. Show that p divides $f\left(x_{\text{0}}\text{+}kp\right)$ for all integers k, Obtain a contradiction of the fact that a polynomial of degree n, where $n>\text{1}$ , takes on each value at most n times.]