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subset with any m,n satisfy |m-n| \ge mn/25

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1986 p6

February 17, 2020
combinatoricsSubsetsinequalities

Problem Statement

Assume that M⊂NM \subset N has the property that every two numbers m,nm,n of MM satisfy ∣m−n∣≥mn/25|m-n| \ge mn/25. Prove that the set MM contains no more than 99 elements. Decide whether there exists such set M.
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