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

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Author(s): M. Ayad | F. Luca

Journal: Albanian Journal of Mathematics
ISSN 1930-1235

Volume: 3;
Issue: 3;
Start page: 95;
Date: 2009;
Original page

ABSTRACT
Let $a$ and $b$ be integers such that $x^n+ax+b$ is an irreducible polynomial. We study the number fields ${f Q}[|theta]$,where $heta$ is a root of the above trinomial. We show thatif $nge 5$, then given an algebraic number field ${f K}$of degree $n$, then there are at most finitely many pairs$(a,b)$ such that ${f K}={f Q}[heta]$.
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