The rational solutions with as denominators powers of to the elliptic diophantine equation are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term (-) unit equations with special properties, that are solved by linear forms in real and -adic logarithms.
On détermine les solutions rationnelles de l’équation diophantienne dont les dénominateurs sont des puissances de . 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 (-) unités à quatre termes dotées de propriétés spéciales, que l’on résout par la théorie des formes linéaires en logarithmes réels et -adiques.
@article{JTNB_1997__9_2_281_0, author = {Benjamin M. M. de Weger}, 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}, doi = {10.5802/jtnb.203}, zbl = {0898.11009}, mrnumber = {1617399}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.203/} }
TY - JOUR TI - $S$-integral solutions to a Weierstrass equation JO - Journal de Théorie des Nombres de Bordeaux PY - 1997 DA - 1997/// SP - 281 EP - 301 VL - 9 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.203/ UR - https://zbmath.org/?q=an%3A0898.11009 UR - https://www.ams.org/mathscinet-getitem?mr=1617399 UR - https://doi.org/10.5802/jtnb.203 DO - 10.5802/jtnb.203 LA - en ID - JTNB_1997__9_2_281_0 ER -
Benjamin M. M. de Weger. $S$-integral solutions to a Weierstrass equation. Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 281-301. doi : 10.5802/jtnb.203. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.203/
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