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.

  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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