Let $\phi\_{n}(x)$ be the $n$-th cyclotomic polynomial. What are the restrictions to $n$ (if any) to have $\phi\_{n}(x)$ divides $\phi\_{2n}(x)$ (where division is in $\mathbb{Z}[x]$)?Or is it true that $\frac{\phi\_{2n}(x)}{\phi\_{n}(x)}\in\mathbb{Z}[x]$ for all integers $n$?