A primitive nth$-$root of unity is a number $\backslash$omega in C such that n is the smallest positive

integer for which $\backslash$omega n $=1.$ Show that if

$\backslash$omega $=$ e $2\backslash$pi ki

n for n $>=2$ and k in Z$,$

is a primitive nth$-$root of unity, then

$\backslash$omega a $=\backslash$omega b $$ a $$ b mod n

for all integers a$,$ b$.$