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18

Part of 2004 Iran MO (3rd Round)

Problems(1)

Prime divisors in a set

Source: Iranian National Olympiad (3rd Round) 2004

1/9/2009
Prove that for any n n, there is a subset {a1,…,an} \{a_1,\dots,a_n\} of N \mathbb N such that for each subset S S of {1,…,n} \{1,\dots,n\}, ∑i∈Sai \sum_{i\in S}a_i has the same set of prime divisors.
number theoryleast common multiplenumber theory proposed