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Infinite set with a curious propety

Source: Iberoamerican MO 2024 Day 2 P6

September 23, 2024
number theoryfloor function

Problem Statement

Determine all infinite sets AA of positive integers with the following propety: If a,b∈Aa,b \in A and a≥ba \ge b then ⌊ab⌋∈A\left\lfloor \frac{a}{b} \right\rfloor \in A
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