Archivio Istituzionale della RicercaLet U = (U-n)(n >= 0) be a Lucas sequence and, for every prime number p, let rho(U)(p) be the rank of appearance of p in U, that is, the smallest positive integer k such that p divides U-k, whenever it exists. Furthermore, let d be an odd positive integer. Under some mild hypotheses, we prove an asymptotic formula for the number of primes p <= x such that d divides p(U)(p), as x -> +infinity.
On the divisibility of the rank of appearance of a Lucas sequence / Sanna, Carlo. - In: INTERNATIONAL JOURNAL OF NUMBER THEORY. - ISSN 1793-0421. - 18:10(2022), pp. 2145-2156. [10.1142/S1793042122501093]
On the divisibility of the rank of appearance of a Lucas sequence
Carlo Sanna
2022
Abstract
Let U = (U-n)(n >= 0) be a Lucas sequence and, for every prime number p, let rho(U)(p) be the rank of appearance of p in U, that is, the smallest positive integer k such that p divides U-k, whenever it exists. Furthermore, let d be an odd positive integer. Under some mild hypotheses, we prove an asymptotic formula for the number of primes p <= x such that d divides p(U)(p), as x -> +infinity.
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11583/2970795