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Prime numbers primitive roots and $\Phi$?
the ratio between the primes dividing the sum of its primitive roots and the primes upto a given limit is asked.
Is there a nice criterion whether a prime divides the sum of its primitve roots ?
In a comment, it is mentioned that every prime $4k+1$ has the desired property, but there are more primes doing the job. Additionally, can it be proven that the sum of the primtive roots of a prime $p$ must be congruent to $-1,0$ or $1$ modulo $p$ ?