Find the remainder when is divided by .
Step 1: Expand given number
The given number is
Let us consider
Using binomial expansion we get,
The expansion has all the factors divisible by except .
Step 2: Determine the cyclicity
Hence
when divided by , leaves a remainder of
when divided by , leaves a remainder of
when divided by , leaves a remainder of .
And then the same process of and will continue.
If the given number is of form , a remainder of is obtained.
If the given number is of form , a remainder of is obtained.
If the given number is of form , it leaves a remainder of .
Step 3: Calculate the remainder
The number given is
Let us find out .
The number is of form .
Hence, the remainder when is divided by is .