### Fields generated by roots of $x^n+ax+b$

*M. Ayad, F. Luca*

#### Abstract

Let $a$ and $b$ be integers such that $x^n+ax+b$ is an irreducible polynomial. We study the number fields ${\bf Q}[\|theta]$,

where $\theta$ is a root of the above trinomial. We show that

if $n\ge 5$, then given an algebraic number field ${\bf K}$

of degree $n$, then there are at most finitely many pairs

$(a,b)$ such that ${\bf K}={\bf Q}[\theta]$.

where $\theta$ is a root of the above trinomial. We show that

if $n\ge 5$, then given an algebraic number field ${\bf K}$

of degree $n$, then there are at most finitely many pairs

$(a,b)$ such that ${\bf K}={\bf Q}[\theta]$.

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