Hi everyone, I would like to ask your help in the following problem, I want to find nonnegative solutions for a system of linear Diophantine equations using some conditions on the constant terms. For example, in the following linear system the variables are x,y_1,y_2,z_1,z_2,w, and n,a,b,c_1,c_2 are nonnegative integers: x+w =a
y_1+y_2+nw=b
y_1+w-z_1=c_1
y_2+w-z_2=c_2
and we have the next conditions for the constants: 0\leq b-an, \;\; 0\leq a-c_1, \;\; 0\leq a-c_2, \;\; \mbox{and} \;\; 0\leq b-c_1-c_2.
I tried to use FindInstance[ ] but I had mistakes even if I don't try to write the conditions for the integers
n,a,b,c_1,c_2:
FindInstance[ x + w == a && y1 + y2 + n w == b && y1 + w - z1 == c1 && y2 + w - z2 == c2 && 0 <= x && 0 <= y1 && 0 <= y2 && 0 <= w && 0 <= z1 && 0 <= z2, {x, y1, y2, w, z1, z2}, Integers]
FindInstance::exvar: "The system contains a nonconstant expression a independent of variables {x,y1,y2,w,z1,z2}"
If I try to add the conditions for the constants, then I obtain the same mistake.
Thanks.