mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 05:39:30 +00:00
0e3ea3fbab
* Replacing the generator with numpy vector operations from lu_decomposition.
* Revert "Replacing the generator with numpy vector operations from lu_decomposition."
This reverts commit ad217c6616.
* Added type annotation.
* Update fermat_little_theorem.py
Used other syntax.
* Update fermat_little_theorem.py
* Update maths/fermat_little_theorem.py
---------
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
31 lines
840 B
Python
31 lines
840 B
Python
# Python program to show the usage of Fermat's little theorem in a division
|
|
# According to Fermat's little theorem, (a / b) mod p always equals
|
|
# a * (b ^ (p - 2)) mod p
|
|
# Here we assume that p is a prime number, b divides a, and p doesn't divide b
|
|
# Wikipedia reference: https://en.wikipedia.org/wiki/Fermat%27s_little_theorem
|
|
|
|
|
|
def binary_exponentiation(a: int, n: float, mod: int) -> int:
|
|
if n == 0:
|
|
return 1
|
|
|
|
elif n % 2 == 1:
|
|
return (binary_exponentiation(a, n - 1, mod) * a) % mod
|
|
|
|
else:
|
|
b = binary_exponentiation(a, n / 2, mod)
|
|
return (b * b) % mod
|
|
|
|
|
|
# a prime number
|
|
p = 701
|
|
|
|
a = 1000000000
|
|
b = 10
|
|
|
|
# using binary exponentiation function, O(log(p)):
|
|
print((a / b) % p == (a * binary_exponentiation(b, p - 2, p)) % p)
|
|
|
|
# using Python operators:
|
|
print((a / b) % p == (a * b ** (p - 2)) % p)
|