TY - JOUR ID - 691370 TI - On some new observations on Kurepa's left factorial JO - Mathematical Analysis and its Contemporary Applications JA - MACA LA - en SN - AU - Fabiano, Nicola AU - Mirkov, Nikola AU - Mitrovic, Zoran D. AU - Radenovic, Stojan AD - Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12--14, 11351 Belgrade, Serbia AD - Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12--14, 11351 Belgrade, Serbia AD - Faculty of Electrical Engineering University of Banja Luka, Patre 5, 78 000, Banja Luka, Bosnia and Herzegovina AD - Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11 120 Beograd 35, Belgrade, Serbia Y1 - 2022 PY - 2022 VL - 4 IS - 3 SP - 1 EP - 8 KW - Left Factorial function KW - Kurepa's function KW - Diophantine equation KW - derangement number KW - reformulation of Kurepa's hypothesis DO - 10.30495/maca.2022.1950392.1047 N2 - 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. UR - https://www.macajournal.com/article_691370.html L1 - https://www.macajournal.com/article_691370_3019c2489e29a0922c9433317c690368.pdf ER -