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On a regular 17-gon

Source: Finnish Mathematics Competition 2002, Final Round, Problem 5

November 14, 2011
geometrycircumcirclemodular arithmeticcombinatorics unsolvedcombinatorics

Problem Statement

There is a regular 1717-gon P\mathcal{P} and its circumcircle Y\mathcal{Y} on the plane. The vertices of P\mathcal{P} are coloured in such a way that A,B∈PA,B \in \mathcal{P} are of diff erent colour, if the shorter arc connecting AA and BB on Y\mathcal{Y} has 2k+12^k+1 vertices, for some k∈N,k \in \mathbb{N}, including AA and B.B. What is the least number of colours which suffices?
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