# Tagged Questions

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### Some types of diophantine equations and their decidability

The MDRP theorem – which answers Hilbert's tenth problem in the negative – says:
There is no algorithm for determining whether an
arbitrary diophantine equation has a solution.
In ...

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### Is there any track for proving $D=NP$, besides showing that $D$ has polynomial-bounded universal quantifiers?

Background
By the MRDP theorem, every for every recursively enumerable set $S$, there exists a Diophantine polynomial $p$ such that
$$x \in S \iff \exists y_1, \dots, y_n \in \mathbb{N} \text{ such ...

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### Reference for original paper (but translated to English) of Matiyasevich's proof of Fibonacci relation being Diophantine?

Hello. I am a maths undergraduate. I am doing a project about history of mathematics. I am looking for the original solution to Hilbert's 10th problem, or at least the theorems that is accessible to ...

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### Weak classes of diophantine functions

From a well-known work(s) by Putnam, Davis, Robinson and Matiyasevich, we know that every partially recursive function is diophantine.
Now it seems a natural question to ask: can we say something ...

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### Why can Diophantine equations represent exponential growth?

The wikipedia page on Matiyasevich's theorem challenges:
Unfortunately there seems to be as yet no short intuitive explanation as to why Diophantine equations can represent exponential growth only ...