Definition:Diophantine Equation

A Diophantine Equation is an indeterminate polynomial equation that allows the variables to be integers. They define an algebraic curve, algebraic surface, or more general object and ask about the lattice points on it.

The term Diophantine refers to Diophantus of Alexandria.

The Fermat Connection
$$x^n + y^n = z^n$$ is a common example of a Diophantine Equation, for which Fermat's Last Theorem was a conjecture regarding its nature of existence.