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

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.

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.

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DOI : https://doi.org/10.5802/jtnb.991
Classification : 11D25,  11D41,  11R16,  11R20,  12F10
Mots clés : Thue equations, simplest cubic fields, simplest sextic fields.
@article{JTNB_2017__29_2_549_0,
     author = {Akinari Hoshi},
     title = {Complete solutions to a family of {Thue} equations of degree~12},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {549--568},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {2},
     year = {2017},
     doi = {10.5802/jtnb.991},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.991/}
}
Akinari Hoshi. Complete solutions to a family of Thue equations of degree 12. Journal de Théorie des Nombres de Bordeaux, Tome 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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