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painting red numbers from 1-100, no number between a,b divides ab

Source: Mathematics Regional Olympiad of Mexico West 2021 P4

September 9, 2022
number theorycombinatoricsColoring

Problem Statement

Some numbers from 11 to 100100 are painted red so that the following two conditions are met: ∙\bullet The number 11 is painted red. ∙\bullet If the numbers other than aa and bb are painted red then no number between aa and bb divides the number abab. What is the maximum number of numbers that can be painted red?
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