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x-y<=xy/25 if x,y in A, max |A|

Source: VJIMC 2001 1.1

July 23, 2021
number theorySetsinequalities

Problem Statement

Let AA be a set of positive integers such that for any x,y∈Ax,y\in A, x>y  ⟹  x−y≥xy25.x>y\implies x-y\ge\frac{xy}{25}.Find the maximal possible number of elements of the set AA.
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