/sci/ - Science & Math

It's been a while since I've done this type of stuff. Please help me.

How did they get that the roots of x^4+x+1 are w,w^2,w^4,w^8 where w is a 15th root of unity?


I know that it's obvious that any root it has will be a 15th root of unity. I know that you could check this by finding a primitive root of unity and testing that its 1st, 2nd, 4th, and 8th powers solve this polynomial. I guess what I'm asking is "why do these powers in particular have to be the root of the same polynomial?"