IMO Shortlist 1995 problem NC6
Dodao/la:
arhiva2. travnja 2012. Let
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
be an odd prime number. How many
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
-element subsets
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
of
![\{1,2,\cdots \ 2p\}](/media/m/b/6/f/b6f5c8b5d483e954c8c4fc217372a717.png)
are there, the sum of whose elements is divisible by
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
?
%V0
Let $p$ be an odd prime number. How many $p$-element subsets $A$ of $\{1,2,\cdots \ 2p\}$ are there, the sum of whose elements is divisible by $p$?
Izvor: Međunarodna matematička olimpijada, shortlist 1995