How is b = B%p-1

#1

In the video, how can b=B%p-1

#2

Just comparing the terms, please carefully go through the terms and explanation.
Video time : 5:30
Its explained in the video very well how we are getting on to every step of derivation.

#3

I am not able to understand. Is it by taking mod on both sides:
We know that B = a*p-1 + b

Taking mod p-1 on both sides , we get

B % p-1 = (a*p-1 % p-1 + b % p-1) % p-1
B%p-1 = (0 + b%p-1) %p-1
B%p-1 = b?
How can it be equal?

#4

We want that B shall be divided in the form of k(p-1)+c
So that we can apply fermets theoram on first part easily and rest, we need to calculate A^c % p only.
Any number can be written in the form of this
x = a*(x/a) + x%a right?
Take example 16 = 3*(16/3) + 16%3
16 = 3*5 + 1 = 16.

So in the theoram, we are doing the same thing. Substitute (p-1) as a in the above thing.

#5

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