Let be the th cyclotomic polynomial. Show that is a primitive root if and only if .
I suspect NonCommAlg will be the first to bite!
haha ... it's not really a challenge, is it? anyway, if is a primitive root modulo p, then modulo for any 0 < d < p - 1. therefore modulo because
but where the product is over the set thus
conversely, suppose and for some then in we'll have thus
for some then taking (formal) derivative we'll get which is obviously impossible.