# Thread: Factoring with Complex Numbers using Trig

1. ## Factoring with Complex Numbers using Trig

I need help with a problem I'm trying to solve:

In terms of n, what is the highest degree polynomial obtained when factoring xn-yn over the reals.

I have found the answer to be φ(n), but am unable to prove it. Can anybody help?

2. ## Re: Factoring with Complex Numbers using Trig

Originally Posted by jojothebobot
I need help with a problem I'm trying to solve:In terms of n, what is the highest degree polynomial obtained when factoring xn-yn over the reals.
I have found the answer to be φ(n), but am unable to prove it. Can anybody help?
Can you explain what "the highest degree polynomial obtained when factoring xn-yn over the reals" means?
A polynomial is a one variable expression. But you have x & y.

3. ## Re: Factoring with Complex Numbers using Trig

Originally Posted by Plato
A polynomial is a one variable expression. But you have x & y.
Hmm, Wikipedia, MathWorld, PlanetMath and Springer Encyclopedia of Mathematics disagree.

4. ## Re: Factoring with Complex Numbers using Trig

Originally Posted by emakarov
Well there is no universal agreement in mathematical notation on anything.

5. ## Re: Factoring with Complex Numbers using Trig

Well, I too would be surprized to hear that $x^2+ y^2$ is not a polynomial.