If $\displaystyle g.c.d(f(x),g(x))=1$,

where $\displaystyle f(x) \in \mathbb{K}[x]$ and $\displaystyle g(x) \in \mathbb{K}[x]$,

where $\displaystyle \mathbb{K}$ is a field of number.

for $\displaystyle \forall$ $\displaystyle m \in \mathbb{Z}$ and $\displaystyle m>0$

show that:

$\displaystyle g.c.d(f(x^m),g(x^m))=1$