MathDB

\Sigma_{j=0}^{k-1} a_j is divisible by a_k for all indices k < n, in integers

Source: IMAR 2016 p1

September 27, 2018

permutationpermutationsnumber theoryCombinatorial Number Theorydivisible

Problem Statement

Fix an integer

n \ge 3

and let

a_0 = n

. Does there exist a permutation

a_1, a_2,..., a_{n-1}

of the first

n-1

positive integers such that

\Sigma_{j=0}^{k-1} a_j

is divisible by

a_k

for all indices

k < n