Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $1\leq j,r\leq (n-1)$.

share|improve this question
add comment

1 Answer

$cos(\frac{jr\pi}{n}) = 1$ if and only if $\frac{jr\pi}{n} = 2k\pi$ for all $k \in \mathbb{Z}$. In particular, take k=1, So $\frac{jr}{n}=2$ i.e. $jr=2n$ $\Rightarrow$ j divides 2n. So, if j>1 $gcd(j,2n)\neq 1$. if j is 1 it is easy to prove.

share|improve this answer
    
Thanks a lot.................... –  user47929 Nov 3 '12 at 19:22
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.