I have the following linear Diophantine equation.
I wish to know the number of solutions to this equation with the constraint that $a,b,c,d,e,f \ge 0$.
What algorithms or techniques may I apply to find the number of solutions?
I've read some papers using wild ideas like Ehrhart polynomials or some wild summations of vector inner products, but they seem out of reach to my comprehension.
Please don't give me the number of solutions to the equation above, I want to work it out with your advice.