After going through all the reminder chapters/notes on this site I made few points on calculating reminder. Here I am trying to put all those points together so that while approaching the reminder questions we can follow a certain pattern.

Question: what is the reminder when M is divided by N.

1. First Check if N is prime if so then use Fermat’s Little theorem.

If p is a prime then for any integer a we have

a^p = a modulo p.

i.e.  If p is a prime and n is an integer then n^p–n is divisible by p.