Comptes Rendus
no. 9-10
Combinatorics/Number Theory
Partition regularity and the primes
[Régularité de partitions et les nombres premiers]

Présenté par : Jean-Pierre Kahane

Thái Hoàng Lê1
1 Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, TX 78712, USA
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 439-441.

Dans cette Note, on montre, comme une conséquence simple du programme de Green et Tao sur le comptage de configurations linéaires dans les nombres premiers et du travail de Deuber sur la régularité de partitions, que si un système dʼéquations est régulier par rapport aux partitions des nombres entiers, alors il est régulier par rapport aux partitions des ensembles {p−1:p premier} ainsi que {p+1:p premier}. Cela répond à une question de Li et de Pan.

The purpose of this Note is to point out, as a simple yet nice consequence of Green and Taoʼs program on counting linear patterns in the primes and Deuberʼs work on partition regularity, that if a system of equations is partition regular over the positive integers, then it is also partition regular over the sets {p−1:p prime} as well as {p+1:p prime}. This answers a question of Li and Pan.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.04.011

Thái Hoàng Lê 1

1 Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, TX 78712, USA 
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Thái Hoàng Lê. Partition regularity and the primes. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 439-441. doi : 10.1016/j.crma.2012.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.011/

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