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Regional Olympiad - FBH 2016 Grade 10 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

September 22, 2018
Combinatorial Number Theoryremaindersetcombinatorics

Problem Statement

Let AA be a set of 6565 integers with pairwise different remainders modulo 20162016. Prove that exists a subset B={a,b,c,d}B=\{a,b,c,d\} of set AA such that a+b−c−da+b-c-d is divisible with 20162016
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