## Sunday, September 28, 2008

### Modulo Arithmetic – Remainder Theory

This extremely useful article for finding remainders has been contributed to TG by Fundoo Bond, another intelligent TGite. All the CAT 2007/2008 who find this article useful are requested to say thanks to Fundoo Bond for his efforts and this wonderful compilation. If you have some interesting article, funda or helpful information to share, please mail it to us and we will post it by your name- Total Gadha

The problems of finding the remainder are considered the most dreadful among the number theory problems. Fortunately, if we arm ourselves with some basic theorems, we will see that we can turn these mind-boggling problems into sitters and can ensure some easy marks.

I will be trying to share both the theory and the examples in order to make the concepts clearer. Again friends, do keep in mind that I am not a genius to write these theorems on my own. I have learnt them from various sources and I am trying my best to explain you in my own words.

corollary of the Wilson theorem
which will be very useful when solving remainder problems.
From Wilson theorem,
we have (p-1)!%p = (p-1) or -1----(1)
from (1) we can say (p-2)!%p = 1