Could not understand the equation

#1

Could not understand the equation at the current timestamp. Please help me. https://youtu.be/K_UOxtlAIms?t=346

#2

its fermat little theorm . where are you having the problem?

#3

I am getting problem that how is b = B%(p-1)

#4

I hope I’ve cleared your doubt. I ask you to please rate your experience here
Your feedback is very important. It helps us improve our platform and hence provide you
the learning experience you deserve.

On the off chance, you still have some questions or not find the answers satisfactory, you may reopen
the doubt.

#5

No not at all doubt not cleared

#6

hello @ayusdas2000
we know x^(p-1) mod p => 1 if p is prime number…fermant little theorem

now to calculate (a^b) mod p .
we can write b = (p-1) + (p-1) + (p-1) … + k

where k is remainder we are left with. i.e k=b%(p-1)

substituting value of b
(a^b)mod p = a^(p-1 + p-1 + p-1 + p-1 … + k) mod p

now using property a^(x+y) => a^x * a^y

=> ( a^(p-1) * a^(p-1) * a^(p-1) … a^k )mod p

now we know a^(p-1) mod p =1

=> 1 * 1 * 1 …a^k mod p
=> a^k mod p
substituting value of k
=> a^(b%(p-1) ) mod p