Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: p-regularity of the p-adic valuation of the Fibonacci sequence

Speaker: **Luis Medina**, Rutgers University

Date: Thursday, October 22, 2009 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In this talk we present the study of the p-adic valuation of the sequence F_n of Fibonacci numbers from the perspective of regular sequences. We establish that this sequence is p-regular for every prime p and give an upper bound on the rank for primes such that Wall's question has an affirmative answer. We also point out that for primes p = 1,4 mod 5 the p-adic valuation of F_n depends only on the p-adic valuation of n and on the sum modulo p-1 of the base-p digits of n --- not the digits themselves or their order.