Lecture 025

Linear Diophantine Equations (in 2 unknowns)

We know


Task: find all solution to 9x + 15y = 6 Solution:

The Chinese Remainder Theorem (CRT)

Let m_1, m_2, ..., m_r \in \mathbb{Z} be pairwise relative prime, let a_1, a_2, ..., a_r \in \mathbb{Z} The system of linear has a unique solution up to M = m_1m_2...m_r

There will be a unique solution up to the multiple of all congruence m.

More About: https://www.uvm.edu/~cvincen1/files/teaching/spring2017-math255/quadraticequation.pdf

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