# Do these two theorems come from Gauß?

$\underline{Theorem \ 1}$ : The group $(\mathbb{Z}/p\mathbb{Z})^{\times}$ is cyclic and its order is $p-1$.

$\underline{Theorem \ 2}$ : Let $k\ge 1$ an integer and $p$ an odd prime number. Then $p^{k}$ admits a primitive root.

Thanks in advance !

• Interesting. In number theory Gauß has more than $25$ theorems, unbelievable ! And what about the first one ? – Maman Apr 2 '17 at 15:19