IMO 2017 Shortlist N3
Determine all integers n ě 2 with the following property: for any integers a1,a2,...,an whose sum is not divisible by n,...
Category: Number Theory
Problem
Determine all integers n ě 2 with the following property: for any integers a1,a2,...,an
whose sum is not divisible by n, there exists an index 1 ď i ď n su h that none of the numbers
ai,ai ai1,...,ai ai1 ¨¨¨ ai`n´1
is divisible by n. (We let ai “ ai´n when i ą n.)
(Thailand)