Y by Adventure10, Mango247
Let
be a prime number and let
be a set of positive integers that satisfies the following conditions:
(i) the set of prime divisors of the elements in
consists of
elements;
(ii) for any nonempty subset of
, the product of its elements is not a perfect
-th power.
What is the largest possible number of elements in
?


(i) the set of prime divisors of the elements in


(ii) for any nonempty subset of


What is the largest possible number of elements in

This post has been edited 1 time. Last edited by djmathman, May 27, 2018, 3:55 PM
Reason: adjusted wording according to https://anhngq.files.wordpress.com/2010/07/imo-2003-shortlist.pdf
Reason: adjusted wording according to https://anhngq.files.wordpress.com/2010/07/imo-2003-shortlist.pdf