IMO Shortlist 2004 problem N7
Kvaliteta:
Avg: 0,0Težina:
Avg: 9,0 Let be an odd prime and a positive integer. In the coordinate plane, eight distinct points with integer coordinates lie on a circle with diameter of length . 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 .
Izvor: Međunarodna matematička olimpijada, shortlist 2004