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87 lines
2.0 KiB
Python
87 lines
2.0 KiB
Python
"""
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== Carmichael Numbers ==
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A number n is said to be a Carmichael number if it
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satisfies the following modular arithmetic condition:
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power(b, n-1) MOD n = 1,
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for all b ranging from 1 to n such that b and
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n are relatively prime, i.e, gcd(b, n) = 1
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Examples of Carmichael Numbers: 561, 1105, ...
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https://en.wikipedia.org/wiki/Carmichael_number
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"""
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from maths.greatest_common_divisor import greatest_common_divisor
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def power(x: int, y: int, mod: int) -> int:
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"""
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Examples:
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>>> power(2, 15, 3)
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2
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>>> power(5, 1, 30)
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5
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"""
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if y == 0:
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return 1
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temp = power(x, y // 2, mod) % mod
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temp = (temp * temp) % mod
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if y % 2 == 1:
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temp = (temp * x) % mod
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return temp
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def is_carmichael_number(n: int) -> bool:
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"""
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Examples:
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>>> is_carmichael_number(4)
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False
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>>> is_carmichael_number(561)
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True
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>>> is_carmichael_number(562)
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False
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>>> is_carmichael_number(900)
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False
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>>> is_carmichael_number(1105)
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True
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>>> is_carmichael_number(8911)
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True
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>>> is_carmichael_number(5.1)
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Traceback (most recent call last):
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...
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ValueError: Number 5.1 must instead be a positive integer
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>>> is_carmichael_number(-7)
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Traceback (most recent call last):
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...
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ValueError: Number -7 must instead be a positive integer
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>>> is_carmichael_number(0)
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Traceback (most recent call last):
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...
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ValueError: Number 0 must instead be a positive integer
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"""
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if n <= 0 or not isinstance(n, int):
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msg = f"Number {n} must instead be a positive integer"
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raise ValueError(msg)
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return all(
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power(b, n - 1, n) == 1
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for b in range(2, n)
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if greatest_common_divisor(b, n) == 1
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)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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number = int(input("Enter number: ").strip())
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if is_carmichael_number(number):
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print(f"{number} is a Carmichael Number.")
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else:
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print(f"{number} is not a Carmichael Number.")
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