What is the general formula to factoring x^n+1 where n is a natural number?

Question

inkyvoyd · Answer

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

inkyvoyd · Answer

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

nincompoop · Answer

want a book?

inkyvoyd · Answer

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

anonymous · Answer

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 $\pm i$

inkyvoyd · Answer

@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.

inkyvoyd · Answer

or Pis, cause of the repeated multiplication

parthkohli · Answer

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.