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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.

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    This isn't easy at all! You can find some useful references for it [here](http://math.stackexchange.com/questions/33731/do-infinitely-many-points-in-a-plane-with-integer-distances-lie-on-a-line). – 2017-01-17

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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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