Solution: 2017-08 Long arithmetic progression

Does there exist a constant \(\varepsilon>0\) such that for each positive integer \(n\) and each subset \(A\) of \(\{1,2,\ldots,n\}\) with \(\lvert A\rvert<\varepsilon n\), there exists an artihmetic progression \(S\) in \(\{1,2,\ldots,n\}\) such that \( S\cap A=\emptyset\) and \(\lvert S\rvert >\varepsilon n\)?

The best solution was submitted by Huy Tùng Nguyễn (2016학번). Congratulations!

Here is his solution of problem 2017-8.

Alternative solutions were submitted by 조태혁 (수리과학과 2014학번, +3), 위성군 (수리과학과 2015학번, +3), 최인혁 (물리학과 2015학번, +3, solution), 오동우 (수리과학과 2015학번, +3), 최대범 (수리과학과 2016학번, +3), 이본우 (2017학번, +3), 김태균 (수리과학과 2016학번, +3), Ivan Adrian Koswara (전산학부 2013학번, +3), 이재우 (함양고등학교 2학년, +3), 장기정 (수리과학과 2014학번, +2).

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