Albanian Journal of Mathematics (ISNN: 1930-1235), Vol 3, No 3 (2009)

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

M. Ayad, F. Luca


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 ${\bf K}={\bf Q}[\theta]$.

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