## Wednesday, July 6, 2016

During the Fall of 1998 I was researching the algorithms computer scientists use to generate random numbers (called pseudorandom numbers). One of the references I came across was this brief statement in Ivars Peterson's book, The Jungles of Randomness: A Mathematical Safari.

“At the heart of the Marsaglia-Zaman method of generating random numbers is the so-called Fibonacci sequence…"

While waiting to see my bone doctor one morning, I remembered this statement and began to explore the patterns exhibited by the one's digit of the Fibonacci sequence. The question in my mind was, What is there about the one’s digit of the Fibonacci sequence that would interest two research mathematicians?

Using only pencil and paper I soon made two startling discoveries (known to others but unknown to me, and probably you) about the 1's digit of any Fibonacci number. My first discovery made it possible for me to write an algorithm that computes the 1’s digit of the nth Fibonacci number.
1. 2. 