We consider a parametric non-Galois family of Thue equations of degree where is an integral parameter and is a divisor of . Using the field isomorphism method which is developed in [15], we show that the equations have only the trivial solutions with .
We considérons une famille paramétrique non galoisienne d’équations de Thue de degré où est un paramètre entier et où est un diviseur de . En utilisant la méthode d’isomorphismes de corps développée dans [15], nous montrons que ces équations ont seulement des solutions triviales avec .
Revised:
Accepted:
Published online:
Keywords: Thue equations, simplest cubic fields, simplest sextic fields.
Akinari Hoshi 1
@article{JTNB_2017__29_2_549_0, author = {Akinari Hoshi}, title = {Complete solutions to a family of {Thue} equations of degree~12}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {549--568}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {29}, number = {2}, year = {2017}, doi = {10.5802/jtnb.991}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.991/} }
TY - JOUR AU - Akinari Hoshi TI - Complete solutions to a family of Thue equations of degree 12 JO - Journal de théorie des nombres de Bordeaux PY - 2017 SP - 549 EP - 568 VL - 29 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.991/ DO - 10.5802/jtnb.991 LA - en ID - JTNB_2017__29_2_549_0 ER -
%0 Journal Article %A Akinari Hoshi %T Complete solutions to a family of Thue equations of degree 12 %J Journal de théorie des nombres de Bordeaux %D 2017 %P 549-568 %V 29 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.991/ %R 10.5802/jtnb.991 %G en %F JTNB_2017__29_2_549_0
Akinari Hoshi. Complete solutions to a family of Thue equations of degree 12. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 2, pp. 549-568. doi : 10.5802/jtnb.991. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.991/
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