Comments on: Generating Fibonacci: Part II http://samjshah.com/2008/04/24/generating-fibonacci-part-ii/ Tue, 15 May 2012 22:49:27 +0000 hourly 1 http://wordpress.com/ By: disquisitionesmathematicae http://samjshah.com/2008/04/24/generating-fibonacci-part-ii/#comment-984 Wed, 06 May 2009 12:54:41 +0000 http://samjshah.wordpress.com/?p=140#comment-984 Sorry,
g_{n}=2^{n}-1

]]> By: disquisitionesmathematicae http://samjshah.com/2008/04/24/generating-fibonacci-part-ii/#comment-982 Wed, 06 May 2009 12:53:02 +0000 http://samjshah.wordpress.com/?p=140#comment-982 After reading this post, I got interested in trying this approach to prove the following theorem,

If\ 2^{n}-1\ is\ prime,\ then \ n\ is\ prime.

I tried to exploit the fact that

g_{n}=2g_{n-1}+1 where g_{n-1}=2^{n}-1

The generating function has the form,

p(x)=\frac{x}{(x-1)(2x-1)}

Any suggestions on how to move further?

]]> By: disquisitionesmathematicae http://samjshah.com/2008/04/24/generating-fibonacci-part-ii/#comment-975 Tue, 05 May 2009 14:24:08 +0000 http://samjshah.wordpress.com/?p=140#comment-975 Beautiful !

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