Remainder Theorem

Rule (1)

if a number is form this type (a+1)ⁿ / a then the remainder is always 1

Rule (2)

if a number is form of a / (a+1)ⁿ then we have two condition

1. if the power n is even then the remainder is always 1.

2. If the power n is odd then the remainder is always a-1.

Rule (3)

if the number is this type aⁿ + (a+4)ⁿ / (a+2) and the n is an even power then the remainder is always 2.

Rule (4)

Lemma theorem:

As the lemma theorem remainder is always equal and less then the divider

d ) a ( q

------------------

r

now the lemma theorem d ≥ r < a

remainder is rqual to divider and less but not greater then a, here one thing is when remainder equal to d remainder is 0 because it divide by d fully.

Rule (5)

Who many possible remainder when we divide any number:

If we divide 12 by 4 then we have only 4 remainder 0,1,2,3 and 4 is also 0.

So the possible remainder is always equal to number and value is 0 to n-1.