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Generalized Fibonacci Primitive Roots

This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.
arxiv.org

Prescribed Primitive Roots And The Least Primes

Let $q\ne \pm1,v^2$ be a fixed integer, and let $x\geq 1$ be a large number. The least prime number $p \geq3 $ such that $q$ is a primitive root modulo $p$ is conjectured to be $p\ll (\log q)(\log \log q)^3),$ where $\gcd(p,q)=1$. This note proves the existence of small primes $p\ll(\log x)^c$, where $c>0$ is a constant, a close approximation to the conjectured upper bound.
arxiv.org

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