10.30495/maca.2022.1950392.1047

On some new observations on Kurepa's left factorial

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  • Nicola Fabiano1,
  • Nikola Mirkov1,
  • Zoran D. Mitrovic2,
  • Stojan Radenovic3,
  1. Vinca Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovica Alasa 12-14, 11351 Belgrade, Serbia
  2. Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina
  3. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd 35, Belgrade, Serbia

Published in Issue 2022-04-01

How to Cite

On some new observations on Kurepa’s left factorial. (2022). Mathematical Analysis and Its Contemporary Applications, 4(3). https://doi.org/10.30495/maca.2022.1950392.1047

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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
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