SOME NEW IDENTITIES CONCERNING GENERALIZED FIBONACCI AND 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 asV2mn+r ? (-(-t) m) n Vr (mod Vm), U2mn+r ? (- (-t) m) nUr (mod Vm), and V2mn+r ? (-t) mn Vr (mod Um), U2mn+r ? (-t) mn Ur (mod Um).