alexmahone
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Is it true that $g$ is a primitive root modulo $p$ if and only if $g^{(p-1)/2} \equiv -1 \pmod p$?
No. For example, take $p=7$ and $g=6$. The congruence is satisfied, but $6$ is not a primitive root$\mod 7$.Alexmahone said:Is it true that $g$ is a primitive root modulo $p$ if and only if $g^{(p-1)/2} \equiv -1 \pmod p$?
Alexmahone said:Is it true that $g$ is a primitive root modulo $p$ if and only if $g^{(p-1)/2} \equiv -1 \pmod p$?