MathDB

5

Part of 2006 IberoAmerican Olympiad For University Students

Problems(1)

Regular n-gon, \prod(5-ai^2)=F_n^2 - OIMU 2006 Problem 5

Source:

8/30/2010
A regular nn-gon is inscribed in a circle of radius 11. Let a1,⋯ ,an−1a_1,\cdots,a_{n-1} be the distances of one of the vertices of the polygon to all the other vertices. Prove that (5−a12)⋯(5−an−12)=Fn2(5-a_1^2)\cdots(5-a_{n-1}^2)=F_n^2 where FnF_n is the nthn^{th} term of the Fibonacci sequence 1,1,2,⋯1,1,2,\cdots
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