.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/number_theory/crt/plot_01_sunzi_problem.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_number_theory_crt_plot_01_sunzi_problem.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_number_theory_crt_plot_01_sunzi_problem.py:


Sunzi's classic "remainder problem"
=========================================

The 3rd-5th-century Chinese text *Sunzi Suanjing* poses: "There are
certain things whose number is unknown. Repeatedly divided by 3, the
remainder is 2; by 5 the remainder is 3; by 7 the remainder is 2. What
is the number?" -- the original problem the Chinese Remainder Theorem
is named for.

.. GENERATED FROM PYTHON SOURCE LINES 13-15

.. code-block:: Python

    from mathematicskit.number_theory import chinese_remainder_theorem








.. GENERATED FROM PYTHON SOURCE LINES 16-18

Solve Sunzi's problem
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 18-24

.. code-block:: Python


    result = chinese_remainder_theorem(remainders=[2, 3, 2], moduli=[3, 5, 7])
    print(f"x = {result.residue} (mod {result.modulus})")

    for r, m in zip([2, 3, 2], [3, 5, 7]):
        print(f"  {result.residue} mod {m} = {result.residue % m} (expected {r})")




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    x = 23 (mod 105)
      23 mod 3 = 2 (expected 2)
      23 mod 5 = 3 (expected 3)
      23 mod 7 = 2 (expected 2)





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.000 seconds)


.. _sphx_glr_download_api_gallery_number_theory_crt_plot_01_sunzi_problem.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_sunzi_problem.ipynb <plot_01_sunzi_problem.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_sunzi_problem.py <plot_01_sunzi_problem.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_sunzi_problem.zip <plot_01_sunzi_problem.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_