<s>[INST] Is $x+1$ a factor of $x^{2016}-1$? $$x^{2016}-1=(x-1)(1+x+x^2+x^3+\dots+x^{2015})$$
If $x+1$ is a factor of $x^{2016}-1$, then $(1+x+x^2+x^3+\dots+x^{2015})=(x+1)G(x)$, where $G(x)$ is some polynomial.
What is $G(x)$ if $x+1$ is also a factor?
 [/INST] \begin{align}
x^{2016}-1=&(x^2)^{1008}-1=(x^2-1)((x^2)^{1007}+\dots+x^2+1)\\
&=(x+1)(x-1)(x^{2014}+\dots+x^2+1).
\end{align}
</s>