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31 lines
831 B
Python
31 lines
831 B
Python
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# 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 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, n, mod):
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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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