Divisibility of sums of subsets
Source: Czech and Slovak Olympiad 2015, National Round, Problem 6
April 1, 2015
Divisibilitynumber theorycombinatoricspigeonhole principle
Problem Statement
Integer is given. Find the biggest integer , for which holds, that from any set consisting of integers, we can find three different (but not necesarilly disjoint) nonempty subsets, such that sum of elements of each of them is divisible by .