Prove that for any positive integer n, there exists at least one multiple of 5^n that doesn't have any perfect cube digits (0, 1, or 8) in its decimal representation.

I am guessing that the actual solution has not been posted by anyone yet.  If it has been posted, I didn't get it.

I'm curious as to how this can be proven. 

Still just hoping I understand the answer.

Posted by Bruce Brantley on 2004-09-20 10:45:26