ISL 2003 N8

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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Solutions

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