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

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