MathDB
Miklos Schweitzer 1973_4

Source:

November 12, 2008
limitlogarithmsnumber theory proposednumber theory

Problem Statement

Let f(n) f(n) be that largest integer k k such that nk n^k divides n! 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