Nobody asked, shame! What is the proof? Best regards, jj P.S.: broke the thread in order to not bury this in old-ish messages. * Tomas Rokicki <rokicki@gmail.com> [Sep 04. 2016 19:07]:
David Wilson's assertion that
The number of zeroes at the end of n! is equal in bases 10 and 16 iff
0 <= sum of base-5 digits of n - sum of base-2 digits of n <= 3.
has a very sweet proof! I admit I started looking for a counterexample before a proof, but I should have had more faith.
I'm omitting the proof because I don't want to spare anyone else the joy of discovery.
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