Mordell equation

This article is about a polynomial Diophantine equation: a Diophantine equation that equates a polynomial in the variables to zero.
View a complete list of polynomial Diophantine equations

Statement

The Mordell equation with parameter $k$ is the following polynomial Diophantine equation:

$y^{2}=x^{3}+k$,

with $k$ a nonzero integer.

Every Mordell equation has only finitely many solutions.

Relation with other properties

Weaker properties

• Thue equation: A Thue equation is an equation of the form $f(x,y)=k$ where $f$ is an irreducible bivariate form of degree at least $3$. Every Thue equation has only finitely many solution.