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Source: French TST 2004, pb.6

May 25, 2004
inductionnumber theoryprime numbersnumber theory solved

Problem Statement

Let PP be the set of prime numbers. Consider a subset MM of PP with at least three elements. We assume that, for each non empty and finite subset AA of MM, with A≠MA \neq M, the prime divisors of the integer (∏p∈A)−1( \prod_{p \in A} ) - 1 belong to MM. Prove that M=PM = P.
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