9-Modularity and GCD Properties of Generalized Fibonacci Numbers (2014)
ABSTRACT: We study 9-modularity properties of generalized Fibonacci numbers that give rise to well-known quasigroups. In this paper we also study GCD and divisibility properties of generalized Fibonacci numbers. This study includes necessary and su cient conditions to determine whether the GCD of two generalized Fibonacci numbers is a regular Fibonacci number.