On the Base-b Expansion of the Number of Trailing Zeros of b!
نویسنده
چکیده
Let Zb(n) denote the number of trailing zeroes in the base-b expansion of n!. In this paper we study the connection between the expression of θ(b) := limn→∞ Zb(n)/n in base b, and that of Zb(b ). In particular, if b is a prime power, we will show the equality between the k digits of Zb(b ) and the first k digits in the fractional part of θ(b). In the general case we will see that this equality still holds except for, at most, the last ⌊logb(k) + 3⌋ digits. We finally show that this bound can be improved if b is square-free and present some conjectures about this bound.
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