Fifty years of Kurepa's $!n$ hypothesis

Žarko Mijajlović

Djuro Kurepa formulated in 1971 the so called left factorial hypothesis. This hypothesis is still open, despite much efforts to solve it. Here we give some historical notes and review the current status of the hypothesis. Using probabilistic model we also estimated sums of Kurepa reminders and discussed in details finite Kurepa trees.