PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On the solvability of an Eisenstein trinomial of prime degree

Volume 178 / 2017

Chahrazede Bouyacoub, Alain Salinier Acta Arithmetica 178 (2017), 385-396 MSC: 11R32, 12F10. DOI: 10.4064/aa8581-10-2016 Published online: 26 April 2017


Let $f(X) = X^p + a c^{p-2} X + a c^{p-1}$ be a trinomial of prime degree $p \ge 7$ that is Eisenstein with respect to $p$, where $a$ and $c$ are coprime rational integers. We investigate the following question, linked to a conjecture formulated by Kölle and Schmid: is it possible for $f(X)$ to be solvable over $\mathbb{Q}$? The main tool in this study is the determination of the decomposition group at a place above some primes that do not ramify in the splitting field of $f(X)$.


  • Chahrazede BouyacoubLaboratoire d’Arithmétique, Codage,
    Combinatoire et Calcul formel
    BP 32, El Alia, Bab Ezzouar 16111
    Alger, Algeria
  • Alain SalinierPôle de Mathématiques et Informatique
    Laboratoire XLIM (UMR CNRS 7252)
    Université de Limoges
    123, avenue Albert Thomas
    87060 Limoges Cedex, France

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image