théorème de Fermat

bonjour, s’il vous plait j’ai une question dans un problème dans lequel on a Montré que l’anneau (Z/nZ, +, ·) est un corps si et seulement si n est premier. Et aprés , ils nous demandent de montrer que a^p est congrue à a module p , tels que a appartient à Z et p est premier , on doit prouver ceci en utilisant le premier resultat . j’ai trop essayé mais je n’est pas arrivé :frowning: ; quelqu’un peut m’aider ??

salut

l’ensemble Z/nZ est fini
l’ensemble E = {a^k / k \in Z } est infini (avec a \ne 1)

comment se peut-il que E \subset Z ?

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