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At least One pair with square of distance multiple of 2016

Source: 38th Brazilian MO (2016) - First Day, Problem 2

November 23, 2016
combinatoricscombinatorial geometryBrazilian Math OlympiadBrazilian Math Olympiad 2016number theory

Problem Statement

Find the smallest number nn such that any set of nn ponts in a Cartesian plan, all of them with integer coordinates, contains two poitns such that the square of its mutual distance is a multiple of 20162016.
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