Polynomial Diophantine equation

Definition

In one variable

The term polynomial Diophantine equation is used for a Diophantine equation of the form:

$\!a_{n}x^{n}+a_{n-1}x^{n-1}+\dots +a_{1}x+a_{0}=0$

where all the coefficients are in the ring of integers $\mathbb {Z}$, and we are interested in solving for $x\in \mathbb {Z}$.

In multiple variables

Fill this in later