On the Base-b Expansion of the Number of Trailing Zeros of (b^k)!

摘要

Let denote the number of trailing zeroes in the base- expansion of . In this paper we study the connection between the expression of in base , and that of . In particular, if is a prime power, we will show the equality between the digits of and the first digits in the fractional part of . In the general case we will see that this equality still holds except for, at most, the last digits. We finally show that this bound can be improved if is square-free and present some conjectures about this bound.