0
$\begingroup$

Let $g$ be a primitive root modulo $p$. Show that all the primitive roots can be obtained from this fixed primitive root as $g^k$ where $1 ≤ k < p$ and $gcd(k, p − 1) = 1$.

Stuck on this problem.

$\endgroup$
0
$\begingroup$

Every nonzero element mod $p$ can be expressed in terms of the primitive root in that way, hence in particular so can the other primitive roots be.

$\endgroup$
  • $\begingroup$ Ahh that makes sense. Thanks. $\endgroup$ – Matt Nov 13 '14 at 22:15
0
$\begingroup$

Hint : Use fermat's little theorem.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.