IMO 2008 Shortlist C2

For every positive integer n determine the number of permutations (a1,a2,...,an) of the set {1,2,...,n} with the followi...

imomathematicsolympiadshortlistcombinatorics

IMO 2008 Shortlist C2

Category: Combinatorics

Problem

For every positive integer n determine the number of permutations (a1,a2,...,an) of the set {1,2,...,n} with the following property: 2(a1 + a2 + ··· + ak) is divisible by k for k = 1,2,...,n.