Hey,

I'm trying to find the period of:

$\displaystyle f(x)=(\cos(\pi\gamma))^{n} \hspace{0,5cm}, \gamma \in \mathbb{R}, n \in \mathbb{N}$

It seems that when $\displaystyle n$ is even then the $\displaystyle f$ has period=1 and when $\displaystyle n$ is odd then $\displaystyle f$ has period=2 .

How to show that analytically?