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