Number theory Diophantine equations Concept
Diophantine equation
Summary
A Diophantine equation is a polynomial equation with integer coefficients, for which one looks for integer solutions, or sometimes rational solutions. Typical questions ask whether a solution exists, whether there are finitely many, and how to find all of them.
Remarks
Examples are the linear equation , Pythagorean triples , Pell's equation and the equation of Fermat's Last Theorem. By Hilbert's tenth problem, as solved by Yuri Matiyasevich in 1970, no algorithm decides for every Diophantine equation whether it has an integer solution. The name refers to Diophantus of Alexandria.
Where this leads
10 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Diophantine_equation, lead section
About this page
| Tag | 08B1RTW7VZ |
|---|---|
| URI | m2://08B1RTW7VZ |
| Kind | concept |
| Writing | W1 stated |
| MSC | 11D99 |
| Same as |
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What this page needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Used by
- Pell's equation
- Fermat's Last Theorem
- Thue equation
- Catalan's conjecture
- Hasse principle
- Hilbert's tenth problem