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a+b-c-d be a multiple of 2013, 6 numbers from a set of 63 < = 2012

Source: Danube 2013 junior p2

July 22, 2019
number theorycombinatoricsmultipleSum

Problem Statement

Consider 6464 distinct natural numbers, at most equal to 20122012. Show that it is possible to choose four of them, denoted as a,b,c,da,b,c,d such that a+b−c−d a+b-c-d to be a multiple of 20132013
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