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Set of primes satisfying property for every proper subset

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July 23, 2012
pigeonhole principlenumber theory proposednumber theory

Problem Statement

Let SS be a nonempty set of primes satisfying the property that for each proper subset PP of SS, all the prime factors of the number (∏p∈Pp)−1\left(\prod_{p\in P}p\right)-1 are also in SS. Determine all possible such sets SS.
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