MathDB
2017 Team #9: Well-centered and decomposable polygons

Source:

February 19, 2017
roots of unitynumber theory

Problem Statement

Let nn be an odd positive integer greater than 22, and consider a regular nn-gon G\mathcal{G} in the plane centered at the origin. Let a subpolygon G′\mathcal{G}' be a polygon with at least 33 vertices whose vertex set is a subset of that of G\mathcal{G}. Say G′\mathcal{G}' is well-centered if its centroid is the origin. Also, say G′\mathcal{G}' is decomposable if its vertex set can be written as the disjoint union of regular polygons with at least 33 vertices. Show that all well-centered subpolygons are decomposable if and only if nn has at most two distinct prime divisors.
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