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.
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On numbers n with polynomial.pdf
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https://hdl.handle.net/11583/2722601