MathDB

Positive integers

m, n

are such that

mn

is divisible by

9

but not divisible by

27

. Rectangle

m \times n

is cut into corners, each consisting of three cells. There are four types of such corners, depending on their orientation; you can see them on the figure below. Could it happen that the number of corners of each type was the exact square of some positive integer?
Proposed by Oleksiy Masalitin
https://i.ibb.co/Y8QSHyf/Kyiv-MO-2023-10-4.png

Problem Statement