Difference between revisions of "2006 OIM Problems/Problem 6"
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| − | Let <math>n > 1</math> be an odd integer. Let <math>P_0</math> and <math>P_1</math> be two consecutive vertices of a regular polygon with <math>n</math> sides. For each <math>k \ge 2</math>, define <math>P_k</math> as the vertex of the given polygon which is located in the bisector of <math>P_{ | + | Let <math>n > 1</math> be an odd integer. Let <math>P_0</math> and <math>P_1</math> be two consecutive vertices of a regular polygon with <math>n</math> sides. For each <math>k \ge 2</math>, define <math>P_k</math> as the vertex of the given polygon which is located in the bisector of <math>P_{k-1}</math> and <math>P_{k-2}</math>. Find for what values of <math>n</math> the sequence <math>P_0, P_1, P_2,\cdots</math>, runs through all the vertices of the polygon. |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 16:08, 14 December 2023
Problem
Let 
be an odd integer. Let 
and 
be two consecutive vertices of a regular polygon with 
sides. For each 
, define 
as the vertex of the given polygon which is located in the bisector of 
and 
. Find for what values of the sequence 
, runs through all the vertices of the polygon.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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