maths.special_numbers.carmichael_number
=======================================

.. py:module:: maths.special_numbers.carmichael_number

.. autoapi-nested-parse::

   == Carmichael Numbers ==
   A number n is said to be a Carmichael number if it
   satisfies the following modular arithmetic condition:

       power(b, n-1) MOD n = 1,
       for all b ranging from 1 to n such that b and
       n are relatively prime, i.e, gcd(b, n) = 1

   Examples of Carmichael Numbers: 561, 1105, ...
   https://en.wikipedia.org/wiki/Carmichael_number



Attributes
----------

.. autoapisummary::

   maths.special_numbers.carmichael_number.number


Functions
---------

.. autoapisummary::

   maths.special_numbers.carmichael_number.is_carmichael_number
   maths.special_numbers.carmichael_number.power


Module Contents
---------------

.. py:function:: 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


.. py:function:: power(x: int, y: int, mod: int) -> int

   Examples:
   >>> power(2, 15, 3)
   2
   >>> power(5, 1, 30)
   5


.. py:data:: number