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distance between 2 of n + 1 points is an integer

Source: 1983 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4

November 22, 2022
distancecombinatoricscombinatorial geometry

Problem Statement

Let gg be a straight line and nn a given positive integer. Prove that there are always n different points on g to choose as well as a point not lying on g in such a way that the distance between each two of these n+1n + 1 points is an integer.
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