Complete solutions of a family of cubic Thue equations
Alain Togbé1
1 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville IN 46391 USA
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 1, pp. 285-298.

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 .

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 .

DOI: 10.5802/jtnb.544
Alain Togbé 1

1 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville IN 46391 USA 
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Alain Togbé. Complete solutions of a family of cubic Thue equations. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 1, pp. 285-298. doi : 10.5802/jtnb.544. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.544/

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