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# Diophantine equations

Diophantine equations are equations requiring integer solutions. For example, ${\displaystyle y^{2}=x^{3}+1}$ 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 ${\displaystyle x^{n}+y^{n}=z^{n}}$; Andrew Wiles finally proved in 1994 that this equation has no integer solutions when ${\displaystyle n>2}$ (see Fermat's last theorem).