Group

Diophantine Equations

This group gathers theorems about integer and rational solutions to polynomial equations, the oldest and broadest branch of number theory, together with the closely related theory of how well irrational numbers can be approximated by fractions. It includes landmark equations such as Fermat's Last Theorem, Pell's equation, and the Catalan and Ramanujan-Nagell equations, the classical technique of infinite descent used to rule out solutions, and the approximation results of Liouville, Thue, Roth, and Schmidt that grew out of the same questions about how closely a number can be pinned down by rationals.

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All Diophantine Equations

Diophantine Equations

30 entries

Diophantine Equations

30 entries

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Sources

1. Diophantine Equation (Wikipedia)

Wikimedia FoundationIntroduction section

Quote, Introduction section

The word Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria.

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Diophantine Equations

All Diophantine Equations

Apery's Theorem

Bhaskara's Lemma

Chevalley-Warning Theorem

Davenport-Schmidt Theorem

Dirichlet's Approximation Theorem

Euler Brick

Fermat's Last Theorem

Hurwitz's Theorem (Number Theory)

Kronecker's Approximation Theorem

Liouville's Approximation Theorem

Lochs' Theorem

Mahler's Compactness Theorem

Mihailescu's Theorem

Pell's Equation

Proof by Infinite Descent

Proof of Fermat's Last Theorem for Specific Exponents

Proof that 22/7 Exceeds Pi

Proof That e Is Irrational

Proof that Pi is Irrational

Ramanujan-Nagell Equation

Ramanujan-Nagell Theorem

Roth's Theorem (Thue-Siegel-Roth)

Schmidt Subspace Theorem

Siegel's Theorem on Integral Points

Skolem-Mahler-Lech Theorem

Sophie Germain's Theorem

Three-Gap Theorem

Thue's Theorem

Tijdeman's Theorem

Wiles's Proof of Fermat's Last Theorem