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 $\mathbb{Z}[x]$)?\mathbb{Z}[x]$)?Or is it true that $\frac{\phi_{2n}(x)}{\phi_{n}(x)}\in\mathbb{Z}[x]$ for all integers $n$?
|
3 | added 91 characters in body | ||
|
|
||||
|
|
2 | added 11 characters in body; added 46 characters in body; added 1 characters in body | ||
|
Let \phi_{n} $\phi_{n}(x)$ be the n-th $n$-th cyclotomic polynomial. What are the restriction restrictions to n $n$ (if any) to have \phi_{n} $\phi_{n}(x)$ divides \phi_{2n} ?$\phi_{2n}(x)$ (where division is in $\mathbb{Z}[x]$)? |
||||
|
|
1 |
|
||
Cyclotomic PolynomialsLet \phi_{n} be the n-th cyclotomic polynomial. What are the restriction to n (if any) to have \phi_{n} divides \phi_{2n} ?
|
||||
