logarithms : prove change of base formula

not exactly... help me prove a bit more challenging statement instead :

If $r$ and $r'$ are both primitive roots of the odd prime $p$, show that for $\gcd(a , p) = 1$
$$\text{ind}_{r'} a = (\text{ind}_r a)(\text{ind}_{r'} r) \pmod{p-1} $$

Question

logarithms : prove change of base formula

not exactly...  help me prove a bit more challenging statement instead :

If $r$ and $r'$ are both primitive roots of the odd prime $p$, show that for $\gcd(a , p) = 1$ 
$$\text{ind}_{r'} a = (\text{ind}_r a)(\text{ind}_{r'} r) \pmod{p-1} $$

rational · Answer

This corresponds to the rule for changing the base of logarithms.

dan815 · Answer

=]

dan815 · Answer

what are primitive roots and do u mean mod (p-1)

rational · Answer

yes it is mod (p-1)

rational · Answer

primitive root of a prime $p$ is an integer $a$ such that $a^{p-1}\equiv  1\pmod{p}$ and $p-1$ is the least such power

rational · Answer

for example  :  $2$ is a primitive root of prime $5$ because $2^{5-1}\equiv  1\pmod 5$ and $5-1$ is the least such power

rational · Answer

another negative example  :  $4$ is NOT a primitive root of prime $5$ because $4^{2}\equiv  1\pmod 5$ and $5-1$ is the NOT the least such power

dan815 · Answer

ok gotcha

dan815 · Answer

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