# Parker Glynn-Adey

## 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.

### One Response

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1. J. H. S. said, on 2013/03/01 at 19:35

My friend,

He forgot to mention this one:

Let f(x) be a non-constant polynomial in Z[x]. Prove that the set

{p in PRIMES: f(n) = 0 mod p, for some n in Z}

is infinite…