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I know that this a likely a relatively elementary problem, but I am a freshman in High School that needs some help.

Let $A$ be an infinite subset of the plane with the property that the distance between any two elements in the set is an integer. Then $A$ is a subset of a line.

E. Joseph
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高田航
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1 Answers1

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The answer of your problem can be find in the book The Art Of Mathematics by Béla Bollobás.

I will post a picture of it here.

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E. Joseph
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