Definition:Diophantine Problem

Definition

A Diophantine problem is a system of Diophantine equations which has more unknowns than it has equations.

Examples

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.

Also see

• Results about Diophantine problems can be found here.

Source of Name

This entry was named for Diophantus of Alexandria.

Historical Note

Diophantus of Alexandria investigated many Diophantine problems in his Arithmetica.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The First Pure Number Puzzles
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Diophantine problem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Diophantine problem