Archivio Istituzionale della RicercaLet F be an integral linear recurrence, G be an integer-valued polynomial splitting over the rationals, and h be a positive integer. Also, let AF,G,h be the set of all natural numbers n such that gcd(F(n), G(n)) = h. We prove that AF,G,h has a natural density. Moreover, assuming F is non-degenerate and G has no fixed divisors, we show that d(AF,G,1) = 0 if and only if AF,G,1 is finite.
On numbers n with polynomial image coprime with the nth term of a linear recurrence / Mastrostefano, Daniele; Sanna, Carlo. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 99:1(2019), pp. 23-33. [10.1017/S0004972718000606]
On numbers n with polynomial image coprime with the nth term of a linear recurrence
Sanna, Carlo
2019
Abstract
Let F be an integral linear recurrence, G be an integer-valued polynomial splitting over the rationals, and h be a positive integer. Also, let AF,G,h be the set of all natural numbers n such that gcd(F(n), G(n)) = h. We prove that AF,G,h has a natural density. Moreover, assuming F is non-degenerate and G has no fixed divisors, we show that d(AF,G,1) = 0 if and only if AF,G,1 is finite.
| File | Dimensione | Formato | |
|---|---|---|---|
|
MastrostefanoSanna.pdf
accesso aperto
Tipologia:
1. Preprint / submitted version [pre- review]
Licenza:
PUBBLICO - Tutti i diritti riservati
Dimensione
335.55 kB
Formato
Adobe PDF
|
335.55 kB | Adobe PDF | Visualizza/Apri |
|
On numbers n with polynomial.pdf
non disponibili
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Non Pubblico - Accesso privato/ristretto
Dimensione
2.68 MB
Formato
Adobe PDF
|
2.68 MB | 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.
https://hdl.handle.net/11583/2722601