论文标题
théorèmedechebotarev et e collence de suitesrécurrenteslinéaires，留置权avec les algorithmes de resconisations sur $ \ mathbb {f} _p $
Théorème de Chebotarev et Congruences de suites récurrentes linéaires, liens avec les algorithmes de factorisations sur $\mathbb{F}_p$
论文作者
论文摘要
斐波那契和卢卡斯序列所满足的经典一致性反映了金数产生的环中的素数分解。这将概括为建立一种信件，我们希望我们将在Chebotarev的定理与线性序列满足的一致性之间是新的。此链接已完成数字字段扩展的上下文。特别是，我们表征了由简单一致性的线性复发序列术语完全分解的素数理想。我们的结果通过许多示例说明了我们的结果，包括$ s_3 $的padovan序列，以及与Cartier Trink多项式相关联，$ \ Mathbb {psl} _2 _2（\ Mathbb {f} _7）$。此外，我们在Berlekamp和Cantor-Zassenhaus的分解算法与这项工作的结果之间建立了联系。
The classical congruences satisfied by the Fibonacci and Lucas sequences are reflected with the decomposition of primes in the ring generated by the gold number. This generalizes to establish a correspondence that we hope will be new between Chebotarev's theorem and the congruences satisfied by linear sequences. This link is done into the context of number field extensions. In particular we characterize primes ideals totally decomposed by simple congruences on the terms of linear recurrent sequences. Our results are illustrated by numerous examples, including Padovan sequencesof group $S_3$ and associated with the Cartier Trink polynomial of group $\mathbb{PSL}_2 (\mathbb{F}_7)$. Furthermore, we establish a link between the factorisation algorithms of Berlekamp and Cantor-Zassenhaus and the results of this work.
