IMO Shortlist 1978 problem 8
Dodao/la:
arhiva2. travnja 2012. Let
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
be the set of all the odd positive integers that are not multiples of
![5](/media/m/e/a/3/ea36c795dac330f34d395d8364d379b6.png)
and that are less than
![30m](/media/m/7/8/9/789383659401f26c821e884119f11c14.png)
,
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
being an arbitrary positive integer. What is the smallest integer
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
such that in any subset of
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
integers from
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
there must be two different integers, one of which divides the other?
%V0
Let $S$ be the set of all the odd positive integers that are not multiples of $5$ and that are less than $30m$, $m$ being an arbitrary positive integer. What is the smallest integer $k$ such that in any subset of $k$ integers from $S$ there must be two different integers, one of which divides the other?
Izvor: Međunarodna matematička olimpijada, shortlist 1978