Brilliant.org - Diophantine Equations
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Brilliant's wiki page on Diophantine equations, explaining linear equations solved with the Euclidean algorithm, Pythagorean triples, and Pell's equation, then using modular arithmetic and factoring to rule out or find integer solutions through worked examples and practice problems.
More resources on Diophantine Equations
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
MathWorld - Diophantine Equation
Wolfram MathWorld's reference entry on Diophantine equations, defining them, surveying linear, Pell, and higher-degree cases, and linking to related results such as Hilbert's tenth problem, with citations to the primary literature for readers who want to follow up on specific equations.
Art of Problem Solving Wiki - Diophantine Equations
Art of Problem Solving's competition-oriented wiki article on Diophantine equations, covering linear equations, Pythagorean triples, Pell equations, and Fermat's Last Theorem, with methods such as modular restrictions and factoring illustrated through contest problems that build olympiad-style solving technique.
Rational Points on Elliptic Curves (2nd edition)
Undergraduate treatment of elliptic curves as Diophantine objects: the group law, Nagell-Lutz, Mordell's theorem, curves over finite fields, integer points, complex multiplication and cryptography. The author's page carries the table of contents and 2024-updated errata.
An Introduction to Diophantine Equations
A problem-based introduction to Diophantine equations covering elementary solving methods (factoring, modular arithmetic, inequalities, parametrization, infinite descent) and classical equations including Pell's and Pythagorean triples, with fully worked solutions aimed at olympiad and Putnam competitors and undergraduates.
Number Theory
Four-week UC San Diego course building from division with remainder and modular arithmetic to Euclid's algorithm and RSA. Finishing it, you can encrypt and decrypt messages and break RSA implementations that reuse or mishandle keys.