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Least element of 2010-set

Source: Costa Rica National Olympiad, Final Round, Problem 6

October 14, 2011
functioncombinatorics unsolvedcombinatorics

Problem Statement

Let FF be the family of all sets of positive integers with 20102010 elements that satisfy the following condition: The difference between any two of its elements is never the same as the difference of any other two of its elements. Let ff be a function defined from FF to the positive integers such that f(K)f(K) is the biggest element of KāˆˆFK \in F. Determine the least value of f(K)f(K).
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