4 problems

Let $f(x)\in\mathbb{Z}[x]$ be a prime-producing polynomial, meaning that it produces infinitely many primes, and let $g\in\mathbb{Z}$. The Artin prime production length $\ell_g(f)$…

Let $f(x)\in\mathbb{Z}[x]$ produce infinitely many primes, and let $g$ be a square-free integer such that all but finitely many primes produced by $f(x)$ remain inert in…

Let $f(x)\in\mathbb{Z}[x]$ produce infinitely many primes. For an integer $g$, define … Here an Artin prime for $g$ is a prime for which $g$ is a primitive root modulo that prime.…

Let $f(x)\in\mathbb{Z}[x]$ produce infinitely many primes. A congruence class modulo a positive integer $m$ is $m$-allowable for $f(x)$ if $(f(r),m)=1$ for every integer $r$ in tha…