Graduate Student Colloquium

Patrick McIntyre, Department of Pure Mathematics, University of Waterloo

"The Pisano Period"

We have all encountered the Fibonacci sequence at some point. It appears everywhere in nature and in any movie that has a math prodigy in it. It has a number of interesting properties. One property that is relatively obscure is that the Fibonacci sequence is periodic mod any integer n. This is known as the Pisano Period, and is denoted pi(n). We will discuss why it has this property, look at some simple examples, examine methods that allow us to indirectly compute the period, and ponder why they didn’t just call it the Fibonacci period.

MC 5501