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Thue equations with composite fields

Yuri Bilu 1 Guillaume Hanrot 2
2 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We consider the Thue equation $F(x,y)=a$, where $F$ is an irreducible form of degree $n\geq 3$.We describe a method of resolution which takes advantage of the fact that the number field generated by a root of $F(1,y)$ has small subfields. We illustrate this method by solving several real cyclotomic equations of degrees as large as 2505. || Considérons l'équation de Thue $F(x,y)=a$, avec $F$ une forme irréductible homogène de degré $n\geq 3$. Nous décrivons une méthode de résolution permettant de tirer profit de l'existence de petits sous-corps du corps de nombres engendré par une racine
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https://hal.inria.fr/inria-00108051
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Submitted on : Thursday, October 19, 2006 - 3:40:29 PM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM

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Yuri Bilu, Guillaume Hanrot. Thue equations with composite fields. Acta Arithmetica, Instytut Matematyczny PAN, 1999, 88 (4), pp.311--326. ⟨inria-00108051⟩

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