tag:blogger.com,1999:blog-9004452969563620551.post4760271734786579145..comments2019-05-15T12:04:42.529+05:30Comments on Paramanand's Math Notes: Gauss and Regular Polygons: Gaussian PeriodsUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-9004452969563620551.post-27240945180136744442014-07-10T01:42:16.714+05:302014-07-10T01:42:16.714+05:30OK, I get it. ThanksOK, I get it. ThanksKazbich-the-bandithttps://www.blogger.com/profile/18247629194967955510noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-77016724185616903352014-07-08T10:13:59.453+05:302014-07-08T10:13:59.453+05:30@Kazbich-the-bandit,
Note that if we take all $n^{...@Kazbich-the-bandit,<br />Note that if we take all $n^{\text{th}}$ roots of unity then these are roots of $x^{n} - 1 = 0$ and hence the sum of these roots is $0$. One of these roots is $x = 1$ and hence the sum of other roots (except $x = 1$) is $-1$. Now in this post we have replaced $n$ with $p$ where $p$ is prime. When $p$ is prime then all roots except $x = 1$ are primitive roots. Hence sum of primitive roots is $-1$. If $p$ was not prime then sum of primitive roots will not be $-1$.Paramanand Singhhttps://www.blogger.com/profile/03855838138519730072noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-68061892955156419802014-07-08T02:31:04.863+05:302014-07-08T02:31:04.863+05:30Hi again, one thing is still bothering me, why is ...Hi again, one thing is still bothering me, why is the sum of the primitive roots = -1?Kazbich-the-bandithttps://www.blogger.com/profile/18247629194967955510noreply@blogger.com