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Regular polygons inscribed in a circle

Source: Russian TST 2016, Day 7 P4

April 19, 2023
combinatorics

Problem Statement

A regular nn{}-gon and a regular mm-gon with distinct vertices are inscribed in the same circle. The vertices of these polygons divide the circle into n+mn+m arcs. Is it always possible to inscribe a regular (n+m)(n+m)-gon in the same circle so that exactly one of its vertices is on each of these arcs?
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