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Tuesday, February 8, 2011

Fibonacci series modulo m

For a while I thought I had discovered some new mathematics. Alas no. Every Coin Has Two Sides. This paper from 1960 by D.D. Wall has no secrets for me. I was well on my way re-discovering and proving until I searched for similar results. I used the Open University library services of course and within a few minutes I found a relevant paper. All this activity is due to NT book 2 from M381.

A Fibonacci series modulo m is cyclic. For example the series mod 3, starting with 0,1 is :
0 1 1 2 0 2 2 1 - 0 1 etc.
and has length 8.

More in the paper.

Dream on. I wished that I could travel back in time. To the year 1914 for example. I would go to Cambridge, England. I would take Number Theory lectures from G.H. Hardy and would make friends with Srinivasa Ramanujan. On the way back to 2011 I would stop the clock somewhere in the midst of World War II, to meet Alan Turing to watch him cracking the Enigma code.

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