The determinant gives an equation with two unknowns. However, if I add another one relating to the next ratio, I obtain a non-homogeneous linear system of equations in the unknowns X and Y, of which there is a solution. What do you think?
Thanks for your time, MFra. I guess we should consider something about: 
Thanks your time again.
Best Regards.
Loi.
I know it's not the answer you are looking for, furthermore, some are negative and aren't diophantine solutions, but it's already something ....
Instead of defining a linear non-homogeneous system of equations with constant coefficients in two variables, in the same way, one should define such a system in N equations in N diophantine unknowns. I don't know if that's possible.
In the group "Gruppo di Matematica" of FB, there is a professor (Domenico Annunziata) who has written a book dedicated to Diophantine equations, you could turn to him for clarification.
