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