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find all n

Source: China South East Mathematical Olympiad 2011

August 18, 2011
combinatorics proposedcombinatorics

Problem Statement

Find all positive integer nn , such that for all 35-element-subsets of M=(1,2,3,...,50)M=(1,2,3,...,50) ,there exists at least two different elements a,ba,b , satisfing : aāˆ’b=na-b=n or a+b=na+b=n.
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