MathDB

We call two simple polygons

P, Q

<span class='latex-italic'>compatible</span>

if there exists a positive integer

k

such that each of

P, Q

can be partitioned into

k

congruent polygons similar to the other one. Prove that for every two even integers

m, n \geq 4

, there are two compatible polygons with

m

and

n

sides. (A simple polygon is a polygon that does not intersect itself.)
Proposed by Hesam Rajabzadeh

Problem Statement