Une démonstration simple du théorème de Skolem-Mahler-Lech

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Abstract

A simple proof of the Skolem-Mahler-Lech theorem is given, which does not make the use of the p-adic number theory. It mainly relies on the equivalence between rational and recognizable series. In particular, this equivalence allows to deduce easily the general case of a commutative field of characteristic zero from the rational case.

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