Monogenic fields arising from trinomials.

We call a polynomial monogenic if a root $\theta$ has the property that $\mathbb{Z}[\theta]$ is the full ring of integers in $\mathbb{Q}(\theta)$. Using the Montes algorithm, we find sufficient conditions for $x^n + ax + b$ and $x^n + cx^{n-1} + d$ to be monogenic (this was first studied by Jakhar, Khanduja, and Sangwan using other methods). Weaker conditions are given for $n = 5$ and $n = 6$. We also show that each of the families $x^n + bx + b$ and $x^n + cx^{n-1} + cd$ are monogenic infinitely often and give some positive densities in terms of the coefficients.