Geodesic
S-integral solutions to a Weierstrass equation
Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 281-301.

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The rational solutions with as denominators powers of 2 to the elliptic diophantine equation y 2 =x 3 -228x+848 are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term (S-) unit equations with special properties, that are solved by linear forms in real and p-adic logarithms.

On détermine les solutions rationnelles de l’équation diophantienne y 2 =x 3 -228x+848 dont les dénominateurs sont des puissances de 2. On applique une idée de Yuri Bilu, qui évite le recours à des équations de Thue et de Thue-Mahler, et qui permet d’obtenir des équations aux (S-) unités à quatre termes dotées de propriétés spéciales, que l’on résout par la théorie des formes linéaires en logarithmes réels et p-adiques.

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     author = {de Weger, Benjamin M. M.},
     title = {$S$-integral solutions to a {Weierstrass} equation},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {281--301},
     publisher = {Universit\'e Bordeaux I},
     volume = {9},
     number = {2},
     year = {1997},
     mrnumber = {1617399},
     zbl = {0898.11009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JTNB_1997__9_2_281_0/}
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de Weger, Benjamin M. M. $S$-integral solutions to a Weierstrass equation. Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 281-301. http://geodesic.mathdoc.fr/item/JTNB_1997__9_2_281_0/

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