Consider the equation $$6x+3y+2z=13$$ for $x$, $y$, $z$ nonnegative integers, with the constraints $$x=0\implies y=0,$$ $$x=0\implies z=0.$$ The set of solutions $(x,y,z)$ is a kind of quasivariety which in this case is $\{(1,1,2)\}$.
Have multivariate linear diophantine equations like this, having a unique solution, been studied in the literature, or do they easily relate to something that has?
