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

Subscribe to comments with RSS.

  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…


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: