A regular polygon with 2007 vertices
Source: Germany Bundeswettbewerb Mathematik 2007, Round 1, Problem 4
May 1, 2007
modular arithmeticgreatest common divisor
Problem Statement
Consider a regular polygon with 2007 vertices. The natural numbers shall be distributed across the vertices and edge midpoints such that for each side the sum of its three numbers (two end points, one side center) has the same value. Show that such an assignment is possible.