Dickson's conjecture on Zn--An equivalent form of Green-Tao's conjecture
Abstract
In [1], we give Dickson's conjecture on Nn. In this paper, we further give Dickson's conjecture on Zn and obtain an equivalent form of Green-Tao's conjecture [2]. Based on our work, it is possible to establish a general theory that several multivariable integral polynomials on Zn represent simultaneously prime numbers for infinitely many integral points and generalize the analogy of Chinese Remainder Theorem in [3]. Dans [1], nous donnons la conjecture de Dickson sur Nn. Dans ce document, en outre nous accordons une conjecture de Dickson sur Zn et obtenons une forme \'equivalent de conjecture de Green-Tao [2]. Sur la base de nos travaux, il est possible d'\'etablir une th\'eorie g\'en\'erale que plusieurs polyn\omes int\'egraux multivariables sur Zn repr\'esentent simultan\'ement les nombres premiers pour un nombre infini de points entiers et de g\'en\'eraliser les l'analogie de Th\'eor\`eme des Restes Chinois dans [3].
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