Colouring rational points
Source: China Team Selection Test 2016 Test 3 Day 1 Q2
March 25, 2016
combinatoricsnumber theoryChina TSTChinaTST
Problem Statement
In the coordinate plane the points with both coordinates being rational numbers are called rational points. For any positive integer , is there a way to use colours to colour all rational points, every point is coloured one colour, such that any line segment with both endpoints being rational points contains the rational points of every colour?