Factorization of polynomial $x^{n}-a^{n}\in\mathbb{C}[x]$ This is my first post here. Mathematics is my hobby. As young I did go through the usual amount of calculus and bit of real analysis. Nowadays I am getting into algebra and more serious analysis.
I have a trouble with this exercise. It goes..
Let $a\in\mathbb{C}$ and $n\in\mathbb{Z}_{+}$. Show that polynomial $x^{n}-a^{n}\in\mathbb{C}[x]$ can be factorized as
$$
x^{n}-a^{n}=\prod_{k=0}^{n-1} (x-e^{\frac{2\pi i k}{n}}a).
$$
I tried to use polynomial division algorithm, but with bad luck. Any hints?

Hints: 


*

*What are the solutions of $x^n = a^n$? In other words, what are the $n^{th}$ roots of $a^n$?

*Use polar representation for $a$: $a = re^{i\theta}$ 
