I actually have a follow-up question to [this post](https://math.stackexchange.com/questions/2513871/complex-numbers-and-pm?noredirect=1#comment5191526_2513871/ "this") -- given that n is a positive integer such that $z^n = (z+1)^n = 1$, I need to show that n is divisible by 6. I can now show that $z$ and $z+1$ both lie on the unit circle, but can this be of any help to me?