Naslov
A Family of the Zeckendorf Theorem Related Identities

Autori
Martinjak, Ivica

Izvornik
International Journal of Applied Mathematics (Sofia) (1311-1728) 28 (2015), 5; 593-603

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Zeckendorf representation; recursive sequence; Fibonacci numbers; Pell numbers; Diophantine equation

Sažetak
In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation. We prove these results using a special case of an universal property of the recursive sequences. In particular cases we also establish a direct bijection. Besides, we prove further equalities that provide a representation of the sum of $(r+1)$-st and $(r-1)$-st Fibonacci number as the sum of powers of the golden ratio. Similarly, we show a class of natural numbers represented as the sum of powers of the silver ratio.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA