  A monogenic polynomial $f$ is a monic irreducible polynomial with integer
coefficients which produces a monogenic number field. For a given prime $q$,
using the Chebotarev density theorem, we will show the density of primes $p$,
such that $t^q-p$ is monogenic, is bigger or equal than $(q-1)/q$. We will also
prove that, when $q=3$, the density of primes $p$, which
$\mathbb{Q}(\sqrt[3]{p})$ is non-monogenic, is at least 1/9.
