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IMO LongList 1985 CZS2 - At most nine elements

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September 10, 2010
number theory proposednumber theory

Problem Statement

Let AA be a set of positive integers such that for any two distinct elements x,y∈Ax, y\in A we have ∣x−y∣≥xy25.|x-y| \geq \frac{xy}{25}. Prove that AA contains at most nine elements. Give an example of such a set of nine elements.
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