IMO Shortlist 1988 problem 20
Dodao/la:
arhiva2. travnja 2012. Find the least natural number
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that, if the set
![\{1,2, \ldots, n\}](/media/m/8/3/2/8329a95a540f5c7a2a5ceff914234e40.png)
is arbitrarily divided into two non-intersecting subsets, then one of the subsets contains 3 distinct numbers such that the product of two of them equals the third.
%V0
Find the least natural number $n$ such that, if the set $\{1,2, \ldots, n\}$ is arbitrarily divided into two non-intersecting subsets, then one of the subsets contains 3 distinct numbers such that the product of two of them equals the third.
Izvor: Međunarodna matematička olimpijada, shortlist 1988