Let f(n) be that largest integer k such that nk divides n!, and let F(n)\equal{} \max_{2 \leq m \leq n} f(m). Show that \lim_{n\rightarrow \infty} \frac{F(n) \log n}{n \log \log n}\equal{}1. P. Erdos limitlogarithmsnumber theory proposednumber theory