Function is_carmichael_number

maths/special_numbers/carmichael_number.py:35–74

Examples: >>> is_carmichael_number(4) False >>> is_carmichael_number(561) True >>> is_carmichael_number(562) False >>> is_carmichael_number(900) False >>> is_carmichael_number(1105) True >>> is_carmichael_number(8911) True >>> is_carmichael_nu

(n: int)

def is_carmichael_number(n: int) -> bool:
    """
    Examples:
    >>> is_carmichael_number(4)
    False
    >>> is_carmichael_number(561)
    True
    >>> is_carmichael_number(562)
    False
    >>> is_carmichael_number(900)
    False
    >>> is_carmichael_number(1105)
    True
    >>> is_carmichael_number(8911)
    True
    >>> is_carmichael_number(5.1)
    Traceback (most recent call last):
         ...
    ValueError: Number 5.1 must instead be a positive integer

    >>> is_carmichael_number(-7)
    Traceback (most recent call last):
         ...
    ValueError: Number -7 must instead be a positive integer

    >>> is_carmichael_number(0)
    Traceback (most recent call last):
         ...
    ValueError: Number 0 must instead be a positive integer
    """

    if n <= 0 or not isinstance(n, int):
        msg = f"Number {n} must instead be a positive integer"
        raise ValueError(msg)

    return all(
        power(b, n - 1, n) == 1
        for b in range(2, n)
        if greatest_common_divisor(b, n) == 1
    )


if __name__ == "__main__":