Diophantine equations

This article page is a stub, please help by expanding it.

---

Diophantine equations are equations requiring integer solutions. For example, $y^{2}=x^{3}+1$ is a Diophantine equation with precisely five solutions: –1, 0; 0, 1; 0, –1; 2, 3; 2, –3. One of the most famous Diophantine equations is $x^{n}+y^{n}=z^{n}$; Andrew Wiles finally proved in 1994 that this equation has no integer solutions when $n>2$ (see Fermat's last theorem).