Determine the remainder when 98! is divided by 101

*** For an extra challenge, solve this problem without using a computer program.

(In reply to Trying to avoid 98 mods... by Jer)

You are correct on the number of zeroes, but I fail to see how this really helps?

As for a shorter way, I've been trying some things, but I can't seem to get very far.

I started with:

98! MOD 101
= (100!/(99*100)) MOD 101

and used the distributive property of MOD:

=((100! MOD 101)/((99*100) MOD 101)) MOD 101

and reduced:

=((100! MOD 101)/(9900 MOD 101)) MOD 101
=((100! MOD 101)/2) MOD 101

Where should I go from here, though?

Edited on September 3, 2011, 4:59 am

Posted by Joshua on 2011-09-02 18:00:41