In mathematics, a Thue equation is a Diophantine equation of the form
where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue who in 1909 proved a theorem, now called Thue's theorem, that a Thue equation has finitely many solutions in integers x and y.
The Thue equation is soluble effectively: there is an explicit bound on the solutions x, y of the form
Solving Thue equations
Solving a Thue equation can be described as an algorithm ready for implementation in software. In particular, it is implemented in the following computer algebra systems: