Complete solutions to a family of Thue equations of degree 12
Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 2, pp. 549-568.

We consider a parametric non-Galois family of Thue equations F m (x,y)=λ of degree 12 where m is an integral parameter and λ is a divisor of 729(m 2 +3m+9). Using the field isomorphism method which is developed in [15], we show that the equations have only the trivial solutions with xy(x+y)(x-y)(x+2y)(2x+y)=0.

We considérons une famille paramétrique non galoisienne d’équations de Thue F m (x,y)=λ de degré 12m est un paramètre entier et où λ est un diviseur de 729(m 2 +3m+9). En utilisant la méthode d’isomorphismes de corps développée dans [15], nous montrons que ces équations ont seulement des solutions triviales avec xy(x+y)(x-y)(x+2y)(2x+y)=0.

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Accepted:
Published online:
DOI: 10.5802/jtnb.991
Classification: 11D25, 11D41, 11R16, 11R20, 12F10
Keywords: Thue equations, simplest cubic fields, simplest sextic fields.

Akinari Hoshi 1

1 Department of Mathematics Niigata University 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Akinari Hoshi. Complete solutions to a family of Thue equations of degree 12. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 2, pp. 549-568. doi : 10.5802/jtnb.991. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.991/

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