$r$ is a primitive root for the prime $p$
$x_1\equiv r^a \pmod{p}$
$x_2\equiv r^b \pmod{p}$
If $gcd(b, p-1)=1$, how can I determine $r$ if $p$, $x_2$, and $b$ are known?
$r$ is a primitive root for the prime $p$
$x_1\equiv r^a \pmod{p}$
$x_2\equiv r^b \pmod{p}$
If $gcd(b, p-1)=1$, how can I determine $r$ if $p$, $x_2$, and $b$ are known?
HINT: If gcd$(b,p-1)=1$, then we can write $1 = tb + s(p-1)$. So $tb\equiv 1 \pmod{p-1}$.
HINT $\ $The isomorphism $\rm n\to r^n\:$ from the additive group $\rm \mathbb Z/(p-1)$ to the multiplicative group $\rm \mathbb Z/p^*\:$
maps $\rm\ b\to x,\ 2b\to x^2,\: \cdots\:,\: nb\to x^n$. You seek $\rm 1\to r\ $ so you need $\rm\ nb\equiv 1\ $ so $\rm\ n\equiv \:\ldots$