MathDB

Two types of tiles, depicted on the figure below, are given. https://wiki-images.artofproblemsolving.com//2/23/Izrezak.PNG
Find all positive integers

n

such that an

n\times n

board consisting of

n^2

unit squares can be covered without gaps with these two types of tiles (rotations and reflections are allowed) so that no two tiles overlap and no part of any tile covers an area outside the

n\times n

board. \\ Proposed by Art Waeterschoot

Problem Statement