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a question of primitive root

Posted: Wed Jun 16, 2021 9:56 am
by rulin
Let $r$ be a prime and $r \geq 19$. Does there exist a prime $p$ in $\left(\dfrac{2r}{3}, r\right)$ such that $r$ is a primitive root mod $p$?

Re: a question of primitive root

Posted: Mon Jun 21, 2021 8:28 pm
by fahim_faiaz_adib
yeah.
consider p=29 , r=31.

that'll do the work

Re: a question of primitive root

Posted: Tue Jun 29, 2021 4:29 pm
by rulin
how to prove that, thanks!