We prove that if (un)n≥0 is a Lucas sequence satisfying some mild hypotheses, then the number of positive integers n does not exceed x and such that n divides un is less than x1−(1/2+o(1)) log log log x/log log x, as x → ∞. This generalizes a result of Luca and Tron about the positive integers n dividing the nth Fibonacci number, and improve a previous upper bound due to Alba Gonz´alez, Luca, Pomerance and Shparlinski

On numbers n dividing the nth term of a Lucas sequence / Sanna, Carlo. - In: INTERNATIONAL JOURNAL OF NUMBER THEORY. - ISSN 1793-0421. - STAMPA. - 13:3(2017), pp. 725-734. [10.1142/S1793042117500373]

On numbers n dividing the nth term of a Lucas sequence

Sanna, Carlo
2017

Abstract

We prove that if (un)n≥0 is a Lucas sequence satisfying some mild hypotheses, then the number of positive integers n does not exceed x and such that n divides un is less than x1−(1/2+o(1)) log log log x/log log x, as x → ∞. This generalizes a result of Luca and Tron about the positive integers n dividing the nth Fibonacci number, and improve a previous upper bound due to Alba Gonz´alez, Luca, Pomerance and Shparlinski
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2722653