Complete solutions of a family of cubic Thue equations
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

 $\begin{array}{cc}\hfill {\Phi }_{n}\left(x,y\right)& ={x}^{3}+\left({n}^{8}+2{n}^{6}-3{n}^{5}+3{n}^{4}-4{n}^{3}+5{n}^{2}-3n+3\right){x}^{2}y\hfill \\ & \phantom{\rule{1em}{0ex}}-\left({n}^{3}-2\right){n}^{2}x{y}^{2}-{y}^{3}=±1,\hfill \end{array}$
for $n\ge 0$.

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

 $\begin{array}{cc}\hfill {\Phi }_{n}\left(x,y\right)& ={x}^{3}+\left({n}^{8}+2{n}^{6}-3{n}^{5}+3{n}^{4}-4{n}^{3}+5{n}^{2}-3n+3\right){x}^{2}y\hfill \\ & \phantom{\rule{1em}{0ex}}-\left({n}^{3}-2\right){n}^{2}x{y}^{2}-{y}^{3}=±1,\hfill \end{array}$
pour $n\ge 0$.

DOI: 10.5802/jtnb.544
Togbé, Alain 1

1 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville IN 46391 USA
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Togbé, Alain. 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. http://archive.numdam.org/articles/10.5802/jtnb.544/

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