Next Article in Journal
Hypersurfaces of a Sasakian Manifold
Next Article in Special Issue
A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers
Previous Article in Journal
A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic
Article

On the Growth of Some Functions Related to z(n)

Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic
Mathematics 2020, 8(6), 876; https://doi.org/10.3390/math8060876
Received: 3 May 2020 / Revised: 25 May 2020 / Accepted: 26 May 2020 / Published: 1 June 2020
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)
The order of appearance z : Z > 0 Z > 0 is an arithmetic function related to the Fibonacci sequence ( F n ) n . This function is defined as the smallest positive integer solution of the congruence F k 0 ( mod n ) . In this paper, we shall provide lower and upper bounds for the functions n x z ( n ) / n , p x z ( p ) and p r x z ( p r ) . View Full-Text
Keywords: asymptotic; arithmetic functions; inequalities; Fibonacci sequence; order of appearance; Landau symbols asymptotic; arithmetic functions; inequalities; Fibonacci sequence; order of appearance; Landau symbols
Show Figures

Figure 1

MDPI and ACS Style

Trojovský, P. On the Growth of Some Functions Related to z(n). Mathematics 2020, 8, 876. https://doi.org/10.3390/math8060876

AMA Style

Trojovský P. On the Growth of Some Functions Related to z(n). Mathematics. 2020; 8(6):876. https://doi.org/10.3390/math8060876

Chicago/Turabian Style

Trojovský, Pavel. 2020. "On the Growth of Some Functions Related to z(n)" Mathematics 8, no. 6: 876. https://doi.org/10.3390/math8060876

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop