maths.extended_euclidean_algorithm
==================================

.. py:module:: maths.extended_euclidean_algorithm

.. autoapi-nested-parse::

   Extended Euclidean Algorithm.

   Finds 2 numbers a and b such that it satisfies
   the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)

   https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm



Functions
---------

.. autoapisummary::

   maths.extended_euclidean_algorithm.extended_euclidean_algorithm
   maths.extended_euclidean_algorithm.main


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

.. py:function:: extended_euclidean_algorithm(a: int, b: int) -> tuple[int, int]

   Extended Euclidean Algorithm.

   Finds 2 numbers a and b such that it satisfies
   the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)

   >>> extended_euclidean_algorithm(1, 24)
   (1, 0)

   >>> extended_euclidean_algorithm(8, 14)
   (2, -1)

   >>> extended_euclidean_algorithm(240, 46)
   (-9, 47)

   >>> extended_euclidean_algorithm(1, -4)
   (1, 0)

   >>> extended_euclidean_algorithm(-2, -4)
   (-1, 0)

   >>> extended_euclidean_algorithm(0, -4)
   (0, -1)

   >>> extended_euclidean_algorithm(2, 0)
   (1, 0)



.. py:function:: main()

   Call Extended Euclidean Algorithm.