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April 9th, 2010, 09:56 PM  #1 
Newbie Joined: Nov 2009 Posts: 6 Thanks: 0  Index of a fibonacci number
Given a fibonacci number, is there any efficient way to compute the its position in the sequence ? I found this on Wikipedia [img] http://upload.wikimedia.org/math/4/6/2/ ... ea259e.png [/img] But when F very large (more than 10000 digits) there wont be sufficient precision to get the answer correctly . Is there any way like matrix exponentiation or something that will get me the answer ? PS: if A= [ [0,1],[1,1] ] .. computing A^n (can be done in O(logn)) will give the nth fibonacci number Thank you 
April 10th, 2010, 02:17 PM  #3 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Index of a fibonacci number
I think you were trying to find the index of the Fibonacci number. Yes, there are a few ways of doing this. Perhaps the easiest way is, 

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