  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.
