IMO Shortlist 2004 problem N7


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2. travnja 2012.
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Let p be an odd prime and n a positive integer. In the coordinate plane, eight distinct points with integer coordinates lie on a circle with diameter of length p^{n}. Prove that there exists a triangle with vertices at three of the given points such that the squares of its side lengths are integers divisible by p^{n+1}.
Izvor: Međunarodna matematička olimpijada, shortlist 2004