The complete solution is usually divided into a sum of two, the solution to the homogeneous equation, i.e., the equation with g(n) = 0, and a particular solution to the equation (4.1) as given.
A set of m solutions f1, . . . , fm to the homogeneous equation (4.1), is called linearly independent, if any equation of the form
cjfj(n) = 0, n ∈ Z (4.2)
has coefficients equal to zero, c1 = · · · = cm = 0.