Questions on finding integer/rational solutions of equations.
This tag is for questions on finding integer/rational solutions of equations.
Diophantine equations are named after Diophantus of Alexandria, a third century Greek mathematician.
In general, a Diophantine equation has more than one variable which makes it impossible to solve just using standard algebra techniques. Methodes that are often used are modular arithmetic, comparing divisiors and infinite descent lower level and elliptic curves at a higher level.
An example of an Diophantine equation: Find all quadruples of integers $(x,y,z,u)$ such that $$x^2+y^2=3(z^2+u^2)$$