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some distinct numbers from the set S = {2,...,111}

Source: 2013 Saudi Arabia GMO TST I p1

July 26, 2020
combinatorics

Problem Statement

Tarik wants to choose some distinct numbers from the set S={2,...,111}S = \{2,...,111\} in such a way that each of the chosen numbers cannot be written as the product of two other distinct chosen numbers. What is the maximum number of numbers Tarik can choose ?
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