Determine the remainder when 98! is divided by 101

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

According to Wilson's Thoerem,

100! mod 101 = 100

=> 99! mod 101 = 1

=> (98! * 99) mod 101 = 1

=> 98! mod 101 = (1/99) mod 101

=> 98! mod 101 = (-1/2) mod 101

=> 98! mod 101 = ((101-1)/2) mod 101

=> 98! mod 101 = 50 mod 101

So, remainder is 50 when 98! is divided by 101

Posted by Praneeth on 2011-09-04 12:07:43