Abstract(s) :
(Anglais) Let Qp be the field of p-adic numbers in the language of rings. In this paper we consider the theory of Qp expanded by two predicates interpreted by multiplicative subgroups αZ and βZ where α,β∈N are multiplicatively independent. We show that the theory of this structure interprets Peano arithmetic if α and β have positive p-adic valuation. If either α or β has zero valuation we show that the theory of (Qp,αZ,βZ)is NIP and therefore does not interpret Peano arithmetic. In that case we also prove that the theory is decidable iff the theory of(Qp,αZ.βZ)is decidable.