## Polynomials

Posted in Math by pgadey on 2013/03/01

Brandon Hanson told me the following elementary number theory problems last night.

Exercise 1 Every non-constant polynomial takes on a composite value.

Hint: Look at ${f(x) = p}$ and ${f(kp + x)}$.

Exercise 2 If a non-constant polynomial takes on infinitely many prime values then it is irreducible.