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Omni-MATH / Let m be a positive integer. A triangulation of a polygon is [i]m-balanced[/i] if its triangles can be colored with m colors in such a way that the sum of the areas of all triangle…

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problem

Let mm be a positive integer. A triangulation of a polygon is [i]mm-balanced[/i] if its triangles can be colored with mm 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 mm colors. Find all positive integers nn for which there exists an mm-balanced triangulation of a regular nn-gon.
Plain-text mathematical notation (without MathML)
Let m be a positive integer. A triangulation of a polygon is [i]m-balanced[/i] 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.
Original LaTeX notation
Let $m$ be a positive integer. A triangulation of a polygon is [i]$m$-balanced[/i] 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.

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Source and history

task_id
c7acc768-33bc-5f63-8366-d00d1fe5d637
task_key
test--c7acc768-33bc-5f63-8366-d00d1fe5d637
task_revision_id
1
config / split
/ test

Official source

initial import