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Coordinate

Source: Iran Third Round MO 1997, Exam 3, P6

October 18, 2005
analytic geometrycombinatorics proposedcombinatorics

Problem Statement

Let P\mathcal P be the set of all points in Rn\mathbb R^n with rational coordinates. For the points A,B∈lPA,B \in \mathcal l{P}, one can move from AA to BB if the distance ABAB is 11. Prove that every point in lP\mathcal l{ P} can be reached from any other point in P\mathcal{P} by a finite sequence of moves if and only if n≥5n \geq 5.
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