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Fix binary_exponentiation: integer exponent and floor division, add doctest #14876

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Fix binary_exponentiation: integer exponent and floor division, add doctest #14876

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14 changes: 12 additions & 2 deletions maths/fermat_little_theorem.py
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Expand Up @@ -5,15 +5,25 @@
# Wikipedia reference: https://en.wikipedia.org/wiki/Fermat%27s_little_theorem


def binary_exponentiation(a: int, n: float, mod: int) -> int:
def binary_exponentiation(a: int, n: int, mod: int) -> int:
"""
Calculate (a ** n) % mod using binary exponentiation, which runs in O(log n) time.

>>> binary_exponentiation(2, 10, 17)
4
>>> binary_exponentiation(3, 0, 5)
1
>>> binary_exponentiation(5, 3, 13)
8
"""
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)
b = binary_exponentiation(a, n // 2, mod)
return (b * b) % mod


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