For a fixed $n\in \mathbb{N}$, prove that
$\cos(\frac{jr\pi}{n})\neq 1$ if and only if $\gcd(j,2n)=1$, where $1\leq j,r\leq (n-1)$.
For a fixed $n\in \mathbb{N}$, prove that
$\cos(\frac{jr\pi}{n})\neq 1$ if and only if $\gcd(j,2n)=1$, where $1\leq j,r\leq (n-1)$.