IMO Shortlist 2003 problem N8
Kvaliteta:
Avg: 0,0Težina:
Avg: 9,0 Let
be a prime number and let
be a set of positive integers that satisfies the following conditions: (1) the set of prime divisors of the elements in
consists of
elements; (2) 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
?
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![p-1](/media/m/3/8/9/389a51fc4e0296668e79f23ead7e404f.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2003