Extremal families of cubic Thue equations
Journal de Théorie des Nombres de Bordeaux, Volume 27 (2015) no. 2, pp. 389-403.

We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form F(x,y)=1 with at least 5 such solutions. Our approach combines elementary arguments, with lower bounds for linear forms in logarithms and lattice-basis reduction.

Nous déterminons les solutions entières d’une nouvelle famille infinie d’équations de Thue cubiques, chacune de ces équations ayant exactement cinq solutions. Notre approche combine des arguments élémentaires avec des limites inférieures pour les formes linéaires en logarithmes et la réduction L 3 .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.907
Classification: 11D25,  11E76
Michael A. Bennett 1; Amir Ghadermarzi 1

1 University of British Coumbia 1984 Mathematics Road Vancouver, B.C. Canada
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Michael A. Bennett; Amir Ghadermarzi. Extremal families of cubic Thue equations. Journal de Théorie des Nombres de Bordeaux, Volume 27 (2015) no. 2, pp. 389-403. doi : 10.5802/jtnb.907. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.907/

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