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Solving Diophantine Equations

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

| | | | created: 2014-02-20 21:51:49 | modified: 2019-06-23 15:48:33 | by: bookofproofs

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

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)