Fibonacci Order of Appearance by Molly FitzGibbons '24

Fibonacci Order of Appearance by Molly FitzGibbons ’24, Monday April 15, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: The order of appearance z(n) of a positive integer n in the Fibonacci sequence is defined as the smallest positive integer j such that n divides the j-th Fibonacci number. A fixed point arises when, for a positive integer n, we have that the n-th Fibonacci number is the smallest Fibonacci that n divides. In other words, z(n) = n. We prove that all positive integers n reach a fixed point after a finite number of iterations. We explore how z applies to other sequences with a Fibonacci recursion and propose future areas for research.