The quotient set of A _ N is defined as R(A) := fa=b : a; b 2 A; b , 0g. Using algebraic number theory inQ(√p5), Garcia and Luca [‘Quotients of Fibonacci numbers’, Amer. Math. Monthly, to appear] proved that the quotient set of Fibonacci numbers is dense in the p-adic numbers Qp for all prime numbers p. For any integer k ≥2, let (F(k)n )n_≥(k-2) be the sequence of k-generalised Fibonacci numbers, defined by the initial values 0, 0,….0, 1 (k terms) and such that each successive term is the sum of the k preceding terms. We use p-adic analysis to generalise the result of Garcia and Luca, by proving that the quotient set of k-generalised Fibonacci numbers is dense in Qp for any integer k _ 2 and any prime number p.

The quotient set of k-generalised Fibonacci numbers is dense in Q_p / Sanna, Carlo. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 96:1(2017), pp. 24-29. [10.1017/S0004972716001118]

The quotient set of k-generalised Fibonacci numbers is dense in Q_p

Sanna, Carlo
2017

Abstract

The quotient set of A _ N is defined as R(A) := fa=b : a; b 2 A; b , 0g. Using algebraic number theory inQ(√p5), Garcia and Luca [‘Quotients of Fibonacci numbers’, Amer. Math. Monthly, to appear] proved that the quotient set of Fibonacci numbers is dense in the p-adic numbers Qp for all prime numbers p. For any integer k ≥2, let (F(k)n )n_≥(k-2) be the sequence of k-generalised Fibonacci numbers, defined by the initial values 0, 0,….0, 1 (k terms) and such that each successive term is the sum of the k preceding terms. We use p-adic analysis to generalise the result of Garcia and Luca, by proving that the quotient set of k-generalised Fibonacci numbers is dense in Qp for any integer k _ 2 and any prime number p.
File in questo prodotto:
File Dimensione Formato  
temp.pdf

accesso aperto

Tipologia: 1. Preprint / submitted version [pre- review]
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 255.6 kB
Formato Adobe PDF
255.6 kB Adobe PDF Visualizza/Apri
The quotient set of k-generalised Fibonacci numbers is dense in Q_p.pdf

non disponibili

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 112.81 kB
Formato Adobe PDF
112.81 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2722651