MathDB

8

Part of 2003 IMO Shortlist

Problems(1)

IMO ShortList 2003, number theory problem 8

Source: IMO ShortList 2003, number theory problem 8

10/4/2004
Let pp be a prime number and let AA be a set of positive integers that satisfies the following conditions:
(i) the set of prime divisors of the elements in AA consists of pāˆ’1p-1 elements;
(ii) for any nonempty subset of AA, the product of its elements is not a perfect pp-th power.
What is the largest possible number of elements in AA ?
modular arithmeticnumber theoryprime numbersPerfect PowersIMO Shortlist