A primitive $n^{th}-$root of unity is a number $inC$ such that $n$ is the smallest positive

integer for which ${}^n=1.$ Show that if

$=e^{\frac{2ki}{n}}$ for $n2$ and kinZ,

is a primitive $n^{th}-$root of unity, then

${}^a={}^b$Longleftrightarrowa$-=b,$modn

for all integers $a,b.$