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,...

IMO 2017 Shortlist N3

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)