Diophantine Problem/Examples

Examples of Diophantine Problems

Arbitrary Example $1$

To find all $x, y \in \Z$ such that:

$11 x + 3 y = 1$

is a Diophantine problem.

Arbitrary Example $2$

To find all $x, y, z \in \Q$ such that:

$x^3 + y^3 = z^3$

is a Diophantine problem.