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assign pairwise different positive integers to vertices of n-gonal prism

Source: Czech-Polish-Slovak Junior Match 2016, individual p3 CPSJ

January 20, 2020
combinatorial geometrycombinatoricsdividesgeometry3D geometryprism

Problem Statement

Find all integers n≥3n \ge 3 with the following property: it is possible to assign pairwise different positive integers to the vertices of an nn-gonal prism in such a way that vertices with labels aa and bb are connected by an edge if and only if a∣ba | b or b∣ab | a.
Poland
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