> 
> Find one integer solution to the Diophantine equation
>  \begin{equation\*}
> 18x+14y+63z=5.
> \end{equation\*}
> 
> 
> 

If this were only a linear equation over $\mathbb{Z}^2$, then I could easily solve it by using the extended Euclidean algorithm... but I have no idea how to do this with more than 2 unknowns...