Nous montrons que, étant donnés et , toute classe inversible modulo contient au moins un produit d’exactement trois nombres premiers, chacun étant inférieur ou égal à .
We prove that, if and are two parameters, then for any invertible residue class modulo there exists a product of exactly three primes, each one below , that is congruent to modulo .
Révisé le :
Accepté le :
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Classification : 11N13, 11A41, 11N37, 11B13
Mots clés : Primes in arithmetic progressions, Least prime quadratic residue, Linnik’s Theorem
@article{JTNB_2018__30_1_219_0,
author = {Olivier Ramar\'e and Aled Walker},
title = {Products of primes in arithmetic progressions: a footnote in parity breaking},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {219--225},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {30},
number = {1},
year = {2018},
doi = {10.5802/jtnb.1024},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1024/}
}
TY - JOUR AU - Olivier Ramaré AU - Aled Walker TI - Products of primes in arithmetic progressions: a footnote in parity breaking JO - Journal de Théorie des Nombres de Bordeaux PY - 2018 DA - 2018/// SP - 219 EP - 225 VL - 30 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1024/ UR - https://doi.org/10.5802/jtnb.1024 DO - 10.5802/jtnb.1024 LA - en ID - JTNB_2018__30_1_219_0 ER -
Olivier Ramaré; Aled Walker. Products of primes in arithmetic progressions: a footnote in parity breaking. Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 1, pp. 219-225. doi : 10.5802/jtnb.1024. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1024/
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