How do I solve a problem with term $a^{n} + b^{n}$? 
Given two non-zero numbers $x$ and $y$ such that $x^{2} + xy + y^{2} = 0$.
Find the value of
$$\left(\frac{x}{x + y}\right)^{2013} + \left(\frac{y}{x + y}\right)^{2013}$$.

I found out that $(x + y)^2 = xy$ and I'm stuck at $\frac{x^{2013} + y^{2013}}{(x + y)^{2013}}$
Does anyone know how to solve this?

$x^3-y^3=(x-y)(x^2+xy+y^2)=0$ $\implies$ $x^3=y^3$
$\left(\dfrac x{x+y}\right)^{2013}=\left(\dfrac{x^2}{x^2+xy}\right)^{2013}=\left(\dfrac{x^2}{-y^2}\right)^{2013}=-\left(\dfrac{x^3}{y^3}\right)^{1342}=-1$
Similarly, $\left(\dfrac y{x+y}\right)^{2013}=-1$.
The sum is $-2$.
