Soit
augmenté de
Par conséquence, en combinant ce résultat avec un résultat récent de Filipin, Fujita et Togbé, nous provons que tous les quadruplets diophantiens de la forme
Let
increased by
Consequently, combining this result with a recent result of Filipin, Fujita and Togbé, we show that all Diophantine quadruples of the form
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1055
Mots-clés : Diophantine
@article{JTNB_2018__30_3_879_0, author = {He, Bo and Pu, Keli and Shen, Rulin and Togb\'e, Alain}, title = {A note on the regularity of the {Diophantine} pair $\protect \lbrace k,4k\pm 4\protect \rbrace $}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {879--892}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {30}, number = {3}, year = {2018}, doi = {10.5802/jtnb.1055}, zbl = {1446.11050}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.1055/} }
TY - JOUR AU - He, Bo AU - Pu, Keli AU - Shen, Rulin AU - Togbé, Alain TI - A note on the regularity of the Diophantine pair $\protect \lbrace k,4k\pm 4\protect \rbrace $ JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 879 EP - 892 VL - 30 IS - 3 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.1055/ DO - 10.5802/jtnb.1055 LA - en ID - JTNB_2018__30_3_879_0 ER -
%0 Journal Article %A He, Bo %A Pu, Keli %A Shen, Rulin %A Togbé, Alain %T A note on the regularity of the Diophantine pair $\protect \lbrace k,4k\pm 4\protect \rbrace $ %J Journal de théorie des nombres de Bordeaux %D 2018 %P 879-892 %V 30 %N 3 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.1055/ %R 10.5802/jtnb.1055 %G en %F JTNB_2018__30_3_879_0
He, Bo; Pu, Keli; Shen, Rulin; Togbé, Alain. A note on the regularity of the Diophantine pair $\protect \lbrace k,4k\pm 4\protect \rbrace $. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 879-892. doi : 10.5802/jtnb.1055. http://www.numdam.org/articles/10.5802/jtnb.1055/
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