On some new observations on Kurepa's left factorial

Fabiano, Nicola; Mirkov, Nikola; Mitrovic, Zoran D.; Radenovic, Stojan

doi:10.30495/maca.2022.1950392.1047

On some new observations on Kurepa's left factorial

https://doi.org/10.30495/maca.2022.1950392.1047

Volume 4, Issue 3
Spring 2022

Pages 1-8

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Nicola Fabiano ¹

Nikola Mirkov ¹

Zoran D. Mitrovic ²

Stojan Radenovic ³

¹ Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12--14, 11351 Belgrade, Serbia

² Faculty of Electrical Engineering University of Banja Luka, Patre 5, 78 000, Banja Luka, Bosnia and Herzegovina

³ Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11 120 Beograd 35, Belgrade, Serbia

Abstract

After a brief historical excursus, we prove in a simple way some properties of Kurepa's function, the left factorial. We introduce Kurepa's hypothesis, propose a new description, and the relation to Bezout's parameters and the Diophantine equation. A numerical analysis supports Kurepa's hypothesis and the conjecture about distribution for Kurepa's function.

Keywords

Left Factorial function

Kurepa's function

Diophantine equation

derangement number

reformulation of Kurepa's hypothesis