# 2017-16 Finding a rectangle

Is it possible to color all lattice points ($$\mathbb Z\times \mathbb Z$$) in the plane into two colors such that if four distinct points $$(a,b), (a+c,b), (a,b+d), (a+c,b+d)$$ have the same color, then $$d/c\notin \{1,2,3,4,6\}$$?

(The next POW problem will be posted on October 20. Happy Chuseok and good luck with your midterm exams.)

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