Some New Identities Concerning Generalized Fibonacciand Lucas Numbers

Authors : Zafer ŞİAR, Refik KESKİN

Pages : 211-222

View : 20 | Download : 8

Publication Date : 2013-03-01

Article Type : Research Paper

Abstract :In this paper we obtain some identities containing generalized Fibonacciand Lucas numbers. Some of them are new and some are well known.By using some of these identities we give some congruences concerninggeneralized Fibonacci and Lucas numbers such asV 2mn+r ≡ insert ignore into journalissuearticles values(−insert ignore into journalissuearticles values(−t);m ); n V r insert ignore into journalissuearticles values(mod Vm );, U 2mn+r ≡ insert ignore into journalissuearticles values(− insert ignore into journalissuearticles values(−t);m ); n U r insert ignore into journalissuearticles values(mod Vm );, and V 2mn+r ≡ insert ignore into journalissuearticles values(−t);mn V r insert ignore into journalissuearticles values(mod Um );, U 2mn+r ≡ insert ignore into journalissuearticles values(−t);mn U r insert ignore into journalissuearticles values(mod Um );.
Keywords : Generalized Fibonacci numbers, Generalized Lucas numbers, 2000 AMS Classification 11B37