MathDB

Let

m

be a positive integer. A triangulation of a polygon is

m

-balanced if its triangles can be colored with

m

colors in such a way that the sum of the areas of all triangles of the same color is the same for each of the

m

colors. Find all positive integers

n

for which there exists an

m

-balanced triangulation of a regular

n

-gon.
Note: A triangulation of a convex polygon

\mathcal{P}

with

n \ge 3

sides is any partitioning of

\mathcal{P}

into

n-2

triangles by

n-3

diagonals of

\mathcal{P}

that do not intersect in the polygon's interior.
Proposed by Krit Boonsiriseth

Problem Statement