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# Diophantine equations and why they are hard

## Snapshots of modern mathematics from Oberwolfach

Diophantine equations and why they are hard

Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. Some Diophantine equations are easy, while some others are truly difficult. After some time spent with these equations, it might seem that no matter what powerful methods we learn or develop, there will always be a Diophantine equation immune to them, which requires a new trick, a better idea, or a refined technique. In this snapshot, we explain why.

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## Mathematical subjects

Algebra and Number Theory

## Connections to other fields

Computer Science

## License

## DOI (Digital Object Identifier)

10.14760/SNAP-2019-003-EN

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## snapshots: overview

## Mathematical subjects

Algebra and Number Theory

Analysis

Didactics and Education

Discrete Mathematics and Foundations

Geometry and Topology

Numerics and Scientific Computing

Probability Theory and Statistics

## Connections to other fields

Chemistry and Earth Science

Computer Science

Engineering and Technology

Finance

Humanities and Social Sciences

Life Science

Physics

Reflections on Mathematics