Determine the remainder when 98! is divided by 101

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

Checking small values (x!>1) returns no remainder if the divisor, d is compound, and the series 2/5, 3/7,5/11,6/13,8/17,9/19... if d is prime.
Since each of these fractions is ((d-1)/2)/d, it follows that the remainder when d=101 is 50.  

Posted by broll on 2011-09-03 00:49:49