Problem of the Week 991

Yet Another Problem on the Digits of n!

For positive integers b and n, let Z(b,n) be the number of trailing zeros when n! is written in base b. Find an integer b so that the limit of n/Z(b,n) as n goes to infinity is 991.

Crux Math, April 2003, Problem 2729, posed by Vaclav Konecny, solved by Natalio Guersenvaig.

© Copyright 2003 Stan Wagon. Reproduced with permission.