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Relatively prime elements

Source: 2004 China Second Round Olympiad

August 30, 2014
number theoryrelatively primenumber theory unsolved

Problem Statement

For integer n≥4n\ge 4, find the minimal integer f(n)f(n), such that for any positive integer mm, in any subset with f(n)f(n) elements of the set m,m+1,…,m+n+1{m, m+1, \ldots, m+n+1} there are at least 33 relatively prime elements.
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