Problem

Source: IMO ShortList 2003, number theory problem 8

Tags: modular arithmetic, number theory, prime numbers, Perfect Powers, IMO Shortlist



Let $p$ be a prime number and let $A$ be a set of positive integers that satisfies the following conditions: (i) the set of prime divisors of the elements in $A$ consists of $p-1$ elements; (ii) 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 $A$ ?


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