IMO Shortlist 2003 problem N8

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Dodao/la: arhiva
2. travnja 2012.
Let p be a prime number and let A be a set of positive integers that satisfies the following conditions: (1) the set of prime divisors of the elements in A consists of p-1 elements; (2) for any nonempty subset of A, the product of its elements is not a perfect p-th power. What is the largest possible number of elements in A ?
Izvor: Međunarodna matematička olimpijada, shortlist 2003