We say that a monic polynomial $f(x)\in { \mathbb Z}[x]$ of degree $N\ge 2$ is monogenic if $f(x)$ is irreducible over ${ \mathbb Q}$ and $\{ 1,\theta,\theta^2,\ldots ,\theta^{ N-1}\}$ is a basis for the ring of integers of ${ \mathbb Q}(\theta)$, where $f(\theta)=0$. In this article, we investigate the divisibility of the class numbers of quadratic fields ${ \mathbb Q}(\sqrt{ \delta})$ for certain families of monogenic trinomials $f(x)=x^N+Ax+B$, where $\delta\ne \pm 1$ is a squarefree divisor of the discriminant of $f(x)$.
Categories: math.NT