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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
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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
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# According to Fermat's little theorem, (a / b) mod p always equals
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# a * (b ^ (p - 2)) mod p
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# Here we assume that p is a prime number, b divides a, and p doesn't divide b
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# Wikipedia reference: https://en.wikipedia.org/wiki/Fermat%27s_little_theorem
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def binary_exponentiation(a: int, n: float, mod: int) -> int:
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if n == 0:
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return 1
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elif n % 2 == 1:
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return (binary_exponentiation(a, n - 1, mod) * a) % mod
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else:
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b = binary_exponentiation(a, n / 2, mod)
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return (b * b) % mod
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# a prime number
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p = 701
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a = 1000000000
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b = 10
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# using binary exponentiation function, O(log(p)):
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print((a / b) % p == (a * binary_exponentiation(b, p - 2, p)) % p)
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# using Python operators:
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print((a / b) % p == (a * b ** (p - 2)) % p)
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