# Remainder Theorem: how to find remainder within seconds, best tricks

## Exam Target

**Remainder
****T****heorem
**

**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 **

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

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

**Rule
(3)**

**if
the number is this type a ^{n}
+ (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.**