On some new observations on Kurepa's left factorial

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