Incoming links: Fermat's last theorem
Sometimes systems of Diophantine equations are considered.
Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.
The general problem is known to be undecidable: Hilbert's tenth problem.
The Pythagorean triples, and its generalization Fermat's last theorem, are the quintessential examples.
Good ones:
- Moving Still (1980); development of film technology
- Race for the Superconductor (1988): recounts the feeding frenzy for high-temperature superconductivity after the Swiss found a ceramic superconductor.
- The Proof (1997): Fermat's last theorem
- Absolute Zero: The Conquest of Cold (2008): cryogenics