## inkyvoyd 2 years ago What is the general formula to factoring x^n+1 where n is a natural number?

1. inkyvoyd

just a general thought question, also I am going to bed so you might want to disregard this one

2. inkyvoyd

but bonus points if you can use full mathematical symbols!!! it'd be such a great learning experience for me :)

3. nincompoop

want a book?

4. inkyvoyd

also, some sort of hint for the dedicated, you could probably reformulate this problem in terms of the nth roots of unity

5. wio

It's easier to think of it as $x^n = -1$So we have two cases. Either $$n$$ is odd, and the roots are just $$-1$$ or $$n$$ is even, and the roots are $$\pm i$$

6. inkyvoyd

@wio , so starting with that I could probably write the solution in terms of 2 sigmas (one for n is odd and one for n is even)? I think I"l try to do this one tomorrow actually. GOod practice for someone like me. THanks guys.

7. inkyvoyd

or Pis, cause of the repeated multiplication

8. ParthKohli

Depends on how you want to factor it. It does have roots that are complex, but it doesn't have real roots, so you can't factorize it.