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Chapter: Solving Diophantine Equations

In this section, we will study Diophantine equations, i.e. equations involving rational numbers or integers, and methods to solve them.

Table of Contents

1. Definition: Diophantine Equations
2. Proposition: Diophantine Equations of Congruences
3. Proposition: Existence of Solutions of an LDE With More Variables
4. Proposition: All Solutions Given a Solution of an LDE With Two Variables
5. Theorem: Chinese Remainder Theorem
6. Proposition: A Linear Term for 1 Using Two Co-prime Coefficients
7. Proposition: Counting the Solutions of Diophantine Equations of Congruences
8. Proposition: Counting the Roots of a Diophantine Polynomial Modulo a Prime Number

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