\begin{definition}[Definition:Diophantine Equation/Linear Diophantine Equation]
A '''linear Diophantine equation''' is a Diophantine equation in which all the arguments appear to no higher than the first degree.
For example:
:$ax + by + c = 0$
:$a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b$
\end{definition}