Complete solutions of a family of cubic Thue equations
Journal de Théorie des Nombres de Bordeaux, Tome 18 (2006) no. 1, pp. 285-298.

Dans cet article, nous utilisons la méthode de Baker, basée sur les formes linéaires en logarithmes, pour résoudre une famille d’équations de Thue liée à une famille de corps de nombres de degré 3. Nous obtenons toutes les solutions de l’équation de Thue

Φ n ( x , y ) = x 3 + ( n 8 + 2 n 6 - 3 n 5 + 3 n 4 - 4 n 3 + 5 n 2 - 3 n + 3 ) x 2 y - ( n 3 - 2 ) n 2 x y 2 - y 3 = ± 1 ,
pour n 0 .

In this paper, we use Baker’s method, based on linear forms of logarithms, to solve a family of Thue equations associated with a family of number fields of degree 3. We obtain all solutions to the Thue equation

Φ n ( x , y ) = x 3 + ( n 8 + 2 n 6 - 3 n 5 + 3 n 4 - 4 n 3 + 5 n 2 - 3 n + 3 ) x 2 y - ( n 3 - 2 ) n 2 x y 2 - y 3 = ± 1 ,
for n 0 .

@article{JTNB_2006__18_1_285_0,
     author = {Togb\'e, Alain},
     title = {Complete solutions of a family of cubic Thue equations},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {285--298},
     publisher = {Universit\'e Bordeaux 1},
     volume = {18},
     number = {1},
     year = {2006},
     doi = {10.5802/jtnb.544},
     mrnumber = {2245886},
     zbl = {05070458},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.544/}
}
Togbé, Alain. Complete solutions of a family of cubic Thue equations. Journal de Théorie des Nombres de Bordeaux, Tome 18 (2006) no. 1, pp. 285-298. doi : 10.5802/jtnb.544. http://www.numdam.org/articles/10.5802/jtnb.544/

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