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Olivier Ramaré; Aled Walker
Products of primes in arithmetic progressions: a footnote in parity breaking
Journal de théorie des nombres de Bordeaux, 30 no. 1 (2018), p. 219-225, doi: 10.5802/jtnb.1024
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Class. Math.: 11N13, 11A41, 11N37, 11B13
Mots clés: Primes in arithmetic progressions, Least prime quadratic residue, Linnik’s Theorem

Résumé - Abstract

Nous montrons que, étant donnés $x$ et $q\leqslant x^{1/16}$, toute classe inversible $a$ modulo $q$ contient au moins un produit d’exactement trois nombres premiers, chacun étant inférieur ou égal à $x^{1/3}$.

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