MathDB
673 element subset has a,b such that 6|a+b

Source: Romanian MO 2010 Grade 7

August 6, 2012
combinatorics proposedcombinatorics

Problem Statement

Let SS be a subset with 673673 elements of the set {1,2,,2010}\{1,2,\ldots ,2010\}. Prove that one can find two distinct elements of SS, say aa and bb, such that 66 divides a+ba+b.