27th Spanish Mathematical Olympiad Problems 1991

Posted in Posted by Unknown on Tuesday, October 5, 2010 at 1:35 AM
A1.  Let S be the set of all points in the plane with integer coordinates. Let T be the set of all segments AB, where A, B ∈ S and AB has integer length. Prove that we cannot find two elements of T making an angle 45o. Is the same true in three dimensions?
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