How can I generate for a given solution of a linear diophantine equation all solutions?
For example let $21x+12y+9z=9$. I found one solution to be $(-3+3t,6-6t,t),t\in\mathbb Z$. How can I generate more solutions, or how can one be sure to have found all solutions?
I am even more interested in the general case for a linear diophantine equation with $n$ variables, i.e. $a_1x_1+\dots a_nx_n=c$. Suppose I have found one solution $(x_1,\dots x_n)$, how I can find all solutions for this equation?
Addendum: I am familiar with the case $n=2$.