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Minimum of maximum element

Source: Greek national M.O. 2004, Final Round,problem 4

November 15, 2011
combinatorics unsolvedcombinatorics

Problem Statement

Let M⊂N∗M\subset \Bbb{N}^* such that ∣M∣=2004.|M|=2004. If no element of MM is equal to the sum of any two elements of M,M, find the least value that the greatest element of MM can take.
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