KöMaL problem A, 2019

Combinatorics Difficulty 6.0 National Olympiad Prove it Hungary

Given are two polyominos, the first one is an L-shape consisting of three squares, the other one contains at least two squares. Prove that if $n$ and $m$ are co-prime then at most one of the $n\times n$ and $m\times m$ boards can be tiled by translated copies of the two polyominos.

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