Soit lʼensemble des entiers positifs ou nul. Pour un sous-ensemble nous notons le nombre de solutions de . La célèbre conjecture dʼErdös–Turán affirme que si pour tout entier , alors nʼest pas borné. Nous montrons dans cette Note quʼil existe un sous-ensemble tel que pour tout entier et tel que lʼensemble des n satisfaisant soit de densité un.
Let be the set of all nonnegative integers. For a set , let denote the number of solutions of with . The well known Erdős–Turán conjecture says that if for all integers , then is unbounded. In this Note, the following result is proved: There is a set such that for all integers and the set of n with has density one.
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Yong-Gao Chen 1
@article{CRMATH_2012__350_21-22_933_0, author = {Yong-Gao Chen}, title = {On the {Erd\H{o}s{\textendash}Tur\'an} conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {933--935}, publisher = {Elsevier}, volume = {350}, number = {21-22}, year = {2012}, doi = {10.1016/j.crma.2012.10.022}, language = {en}, }
Yong-Gao Chen. On the Erdős–Turán conjecture. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 933-935. doi : 10.1016/j.crma.2012.10.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.022/
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☆ This work was supported by the National Natural Science Foundation of China, Grant No. 11071121.
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