Some New Identities Concerning Generalized Fibonacci and Lucas Numbers

Abstract

In this paper we obtain some identities containing generalized Fibonacci and Lucas numbers. Some of them are new and some are well known. By using some of these identities we give some congruences concerning generalized Fibonacci and Lucas numbers such as

V2mn+r equivalent to (-(-t)(m))(n) V-r (mod V-m),

U2mn+r equivalent to (-(-t)(m))(n) U-r (mod V-m),

and

V2mn+r equivalent to (-t)V-mn(r) (mod U-m),U-

U2mn+r equivalent to (-t)(mn) U-r (mod U-m).