IMO Shortlist 1973 problem 4
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 Let
be a set of
different prime numbers and
a set of
different composite numbers each of which is a product of two (not necessarily different) numbers from
. The set
is divided into
disjoint four-element subsets such that each of the numbers in one set has a common prime divisor with at least two other numbers in that set. How many such partitions of
are there ?
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![7](/media/m/5/1/9/519154d5119d15088eebb25b656d58dd.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![28](/media/m/8/a/2/8a23d80865b1d7ff9b4e2d8e34febaee.png)
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![7](/media/m/5/1/9/519154d5119d15088eebb25b656d58dd.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1973