a question of primitive root

For discussing Olympiad Level Number Theory problems
rulin
Posts:2
Joined:Wed Jun 16, 2021 9:48 am
a question of primitive root

Unread post by rulin » Wed Jun 16, 2021 9:56 am

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 $p$?
Last edited by tanmoy on Wed Jun 16, 2021 3:45 pm, edited 1 time in total.

fahim_faiaz_adib
Posts:4
Joined:Tue Jun 01, 2021 10:07 pm

Re: a question of primitive root

Unread post by fahim_faiaz_adib » Mon Jun 21, 2021 8:28 pm

yeah.
consider p=29 , r=31.

that'll do the work

rulin
Posts:2
Joined:Wed Jun 16, 2021 9:48 am

Re: a question of primitive root

Unread post by rulin » Tue Jun 29, 2021 4:29 pm

how to prove that, thanks!

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