Yes.
I would like to find all n where the 2005th digit of n! is 0.
Can we deduce if the possible number of such n is finite? Can we find the pattern?
If n is known, I can do it.
For instance, if n=100, then in n!, the factors 5, 10, 15, 20, ..., 95, 100 involve 5.
So the highest power...