Definition:Diophantine Equation

Definition
A Diophantine equation is an indeterminate polynomial equation that allows the variables to take integer values only.

It defines an algebraic curve, algebraic surface, or more general object, and asks about the lattice points on it.

Also see

 * Fermat's Last Theorem: $x^n + y^n = z^n$ is a well-known example of a Diophantine equation.