IMO Shortlist 2008 problem C2
Dodao/la:
arhiva2. travnja 2012. Let
![n \in \mathbb N](/media/m/4/e/6/4e671e4759f4315f56d66487a7496230.png)
and
![A_n](/media/m/5/2/c/52cc7b12306c4c6a541b1b5322ccf2d6.png)
set of all permutations
![(a_1, \ldots, a_n)](/media/m/8/a/3/8a3ae6c8596bdf745df412087f658d2a.png)
of the set
![\{1, 2, \ldots , n\}](/media/m/c/7/b/c7bb244843a27690de19053c5512d5d8.png)
for which
![k|2(a_1 + \cdots+ a_k), \text{ for all } 1 \leq k \leq n.](/media/m/7/b/1/7b13396771e4f34512c6a9983e518ace.png)
Find the number of elements of the set
%V0
Let $n \in \mathbb N$ and $A_n$ set of all permutations $(a_1, \ldots, a_n)$ of the set $\{1, 2, \ldots , n\}$ for which
$$k|2(a_1 + \cdots+ a_k), \text{ for all } 1 \leq k \leq n.$$
Find the number of elements of the set $A_n.$
Izvor: Međunarodna matematička olimpijada, shortlist 2008