Determine the greatest natural number $n$, such that for each set $S$ of 2015 different integers there exist 2 subsets of $S$ (possible to be with 1 element and not necessarily non-intersecting) each of which has a sum of its elements divisible by $n$.
Problem
Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade
Tags: number theory, set theory, sums