MathDB

Permutations and divisibility

Source: Serbia TST 2009, IMO Shortlist 2008, Combinatorics problem 2

April 17, 2009

combinatoricspermutationDivisibilityIMO Shortlist

Problem Statement

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

.
Proposed by Vidan Govedarica, Serbia