Some New Identities Concerning Generalized Fibonacciand Lucas Numbers

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 ≡ (−(−t)m ) n V r (mod Vm ), U 2mn+r ≡ (− (−t)m ) n U r (mod Vm ), and V 2mn+r ≡ (−t)mn V r (mod Um ), U 2mn+r ≡ (−t)mn U r (mod Um ).