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Alain Togbé
Complete solutions of a family of cubic Thue equations
Journal de théorie des nombres de Bordeaux, 18 no. 1 (2006), p. 285-298, doi: 10.5802/jtnb.544
Article PDF | Reviews MR 2245886 | Zbl 05070458
See also an erratum to this article

Résumé - Abstract

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{@align}{1}{*}{-1} \Phi _n(x,y)&= x^3 + (n^8+2n^6-3n^5+3n^4-4n^3+5n^2-3n+3) x^2 y\\ &\quad - (n^3-2)n^2 x y^2 - y^3 = \pm 1, \end{@align}

for $n\ge 0$.

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