# Math Help - Primitive root help

1. ## Primitive root help

for each m = 7^3 and m = 28

determine whether or not there exists a primitive root mod m, and if so find.

2. Originally Posted by Rakesh
for each m = 7^3 and m = 28
determine whether or not there exists a primitive root mod m, and if so find.
Not for $28$, why not?

There is one for $7^3$. Note $2$ is primitive root for $7$. But $2^{7-1}\equiv 1(\bmod 7^2)$. So $2+7=9$ is primitive root for $7^3$ and $9^{7-1}\not \equiv 1(\bmod 7^2)$.