IMO Shortlist 1994 problem N1
Dodao/la:
arhiva2. travnja 2012. ![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
is a subset of
![\{1, 2, 3, \ldots, 15\}](/media/m/3/5/e/35e4ddfdc29dc834b020163d99ca00e3.png)
such that the product of any three distinct elements of
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
is not a square. Determine the maximum number of elements in
%V0
$M$ is a subset of $\{1, 2, 3, \ldots, 15\}$ such that the product of any three distinct elements of $M$ is not a square. Determine the maximum number of elements in $M.$
Izvor: Međunarodna matematička olimpijada, shortlist 1994